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Arguments |
ARGUMENTS
WITH 3 SIMPLE STATEMENTS
| A | B | C | |||||||||||||||||
| 0 | 0 | 0 | |||||||||||||||||
| 0 | 0 | 1 | |||||||||||||||||
| 0 | 1 | 0 | |||||||||||||||||
| 0 | 1 | 1 | |||||||||||||||||
| 1 | 0 | 0 | |||||||||||||||||
| 1 | 0 | 1 | |||||||||||||||||
| 1 | 1 | 0 | |||||||||||||||||
| 1 | 1 | 1 |
Now that you have mastered arguments with two simple statements,
you are ready to test arguments with three or more simple statements.
EXAMPLE: FOOTBALL PLAYOFFS
Make the truth table for the argument below:
1. The Colts will be in the playoffs if and only if Peyton leads the league in passing.
2. Either Marv loves the Colts, or Peyton leads the league in passing, but not both.
3. Marv does not love the Colts.
4. Therefore, the Colts will not be in the playoffs.
First, identify the simple statements in this argument:
Let A = the Colts will be in the playoffs.
Let B = Peyton leads the league in passing.
Let C = Marv loves the Colts.
Next write each sentence as a compound statement:
Statement 1 is expressed in symbols as A <=> B.
Statement 2 becomes C Å B. (The Å is the EXCLUSIVE OR or XOR.)
Statement 3 is simply —C.
Statement 4 is —A.
Now conjunct all but the last of these statements together in a long compound statement;
and then connect the last statement at the end with an implication. Like this:
[(A <=> B) & (C Å B) & —C] -> —A
If you prefer abbreviations rather than symbols, write the argument like this:
[(A EQV B) AND (C XOR B) AND NOT C] IMP (NOT A)
Now make your table. Refer to your previous notes to combine AND OR NOT IMP XOR EQV.
[(A <=> B) & (C Å B) & —C] —> —A
A B C | [(A EQV B) AND (C XOR B) AND NOT C] IMP (NOT A) (row)
___________________________________________________________________
0 0 0 | 0 1 0 0 0 0 0 0 1 1 1 ( 0 )
0 0 1 | 0 1 0 1 1 1 0 0 0 1 1 ( 1 )
0 1 0 | 0 0 1 0 0 1 1 0 1 1 1 ( 2 )
0 1 1 | 0 0 1 0 1 0 1 0 0 1 1 ( 3 )
1 0 0 | 1 0 0 0 0 0 0 0 1 1 0 ( 4 )
1 0 1 | 1 0 0 0 1 1 0 0 0 1 0 ( 5 )
1 1 0 | 1 1 1 1 0 1 1 1 1 0 0 ( 6 )
1 1 1 | 1 1 1 0 1 0 1 0 1 1 0 ( 7 )
___________________________________________________________________
steps 1 2 1 3 1 2 1 4 1 5 1
|______^______|______^____|
If the implication column (5) is all 1's, then the argument is true under all conditions,
and is therefore valid. Notice, however, that a 0 occurs on row 6.
Therefore, since it is not valid under all values of A, B, and C, the argument is invalid.
HEY! HOLD ON HERE NOW!
This is getting way too complicated for my 85 year old brain!
I need some help.
I know a guy named Brian who wrote an applet to do all this for me.
Brian's applet will do all the tedious stuff for us
if we will translate the statements into symbols.
Click the button that says [Start Truth Table Constructor].
This will download the applet into its own window.
Note that Brian allows you to use alternate symbols for operators:
OURS | BRIAN'S
________________
+ | v or +
& | ^ or &
– | ~ or -
-> | => or ->
<=> | <=> or <->
Å | %
When you enter ((A <=> B) & (C % B) & ~C) => ~A
in Brian's Enter Statement box, and click the OK button, you get this truth table:
If Brian's Evaluation is Identity, then your argument is valid.
When your argument is valid, the red column is all 1's.
If Brian's Evaluation is Conditional, then your argument is invalid.
When your argument is invalid, there is a 0 in the red column.
The football argument fails when A and B are true, but C is false.
Be careful to use parentheses correctly, or your results may not be correct.
Careful: use % only if the OR is exclusive. Use <=> only if IF is an IF AND ONLY IF if.
ASSIGNMENT:
Select one of the arguments below that no one else has previously chosen
and construct the truth table for it.
Use letters that are mnemonic.
Copy the argument number, the simple statements, the symbolic translations,
and the corresponding truth table to a table in a comment below.
Indicate its validity.
CAUTION!
If your simple sentences are not simple on your first try,
I will tell you what they should be;
and you will lose 1 point extra credit.
So read and think before you leap!
A correct analysis of your argument is worth 7 points:
- Write simple statement A (without NOTs ANDs ORs).
- Write simple statement B (without NOTs ANDs ORs).
- Write simple statement C (without NOTs ANDs ORs).
- Write each sentence in the argument as a symbolic statement
(with appropriate NOTs ANDs ORs). - Conjunct (AND &) all Premises into one compound statement,
and then connect the Conclusion with an implication (=>). - Use Brian's Truth Constructor to find the validity of your argument.
- Copy the symbolic argument from Brian's Truth Constructor to a comment,
along with your simple statements,
and the symbolic representation of each sentence in your argument.
To save lots of time, Hoversnap your argument from Brian's Truth Constructor,
and insert it in your comment. Then you don't need to make a table!
Brian's Truth Table Constructor should make this assignment much easier:
You may want to use it on your previous assignments also.
Click here for an Arguments Demo.
1. COUNTRY SONG
If you wuz my woman, an' I wuz yer man, I'd never stop lovin you. But, darlin, I've stopped lovin you. So, you ain't my woman, or I ain't yer man.
2. MISS AMERICA
Either Miss Pennsylvania wins the Miss America Pageant, or Miss Kentucky is first runner up, but not both. However, Miss Kentucky is first runner up if and only if Miss Rhode Island is the second runner up. But Miss Rhode Island is not the second runner up. Therefore, Miss Pennsylvania is not Miss America.
3. JACK
All work and no play made Jack a dull boy. However, since his recent lay off from work, Jack has been playing around a lot. At least he's not so dull anymore. Let W = Jack works. P = Jack plays. D = Jack is dull.
4. FLU
If you catch the flu, you can infect others. Sore throats, however, cannot infect others. But, if sore throats could infect others, you would definitely catch the flu.
5. ELECTION
If Nader wins Arizona and Bush loses Ohio, then Kerry wins the election. But if Bush wins Ohio, Kerry could still win the election if Nader wins Arizona.
6. RUNNING
If Hillary runs, McCain will not. But Hillary will run if Bill tells her to. McCain decides to run. So Bill did not tell Hillary to run.
7. COLUMBUS DAY
Every Columbus Day, Running Fox burns an American flag to mourn the destruction of his Lakota culture. The U.S. Constitution guarantees him this freedom of expression; but, according to the new 28th Amendment, it also forbids flag burning. This Columbus Day, the FBI arrested Running Fox for burning an American flag. According to the U.S. Constitution, Running Fox is both guilty and not guilty.
8. GOLF
Jeff loves to play golf. If Joan likes to sew, then Jeff does not love to play golf. If Joan does not like to sew, then Brad sings in the choir. Therefore, Brad sings in the choir.
9. BEETLES
If that tree is infested with pine bark beetles, then it will die. People plant trees on Arbor Day and it will not die. Therefore, if people plant trees on Arbor Day, then that tree is not infested with pine bark beetles.
10. BARBIE
If the Bobble head doll craze continues, then Beanie Babies will remain popular. Either Barbie dolls will continue to be favorites, or Beanie Babies will remain popular. Assume Barbie dolls wll not continue to be favorites. Then the Bobble head doll craze will not continue.
11. AMERICAN IDOL
Christina Aguilera sings tonite, or Ricky Martin is no longer a teen idol. If Ricky Martin is not a teen idol anymore, then Britney Spears will not win an American Music Award. But Britney Spears does win an American Music Award. Therefore, Christina Aguilera does not sing tonite.
12. OLD STANDARD
When I've got you under my skin, you are deep in the heart of me. When you are deep in the heart of me, you are really a part of me. But either you are deep in the heart of me, or you aren't really a part of me. So, when I've got you under my skin, you really are a part of me.
13. SLIPPED DISC
If Otis is a disk jockey, then he lives in Lexington. He does live in Lexington, and, furthermore, he is a history buff. So, if Otis were not a history buff, he would not be a disc jockey either?
14. BANK
If I write a check it will bounce. If the bank guarantees it, then it will not bounce. The bank will guarantee alright. So I don't write the check.
15. THREE LADIES
If the ladies on the left and in the middle are both lying, then the lady on the right is telling the truth. The lady on the right says that the lady in the middle is lying. If so, then the lady on the left is also lying.
16. THREE LADIES REVISITED
If Ms. Thompson is telling the truth, then Ms. Anderson is in the middle. If Ms. Anderson is in the middle, then Ms. Johnson is on the left. But Ms. Thompson always tells the truth. Therefore, Ms. Anderson must be in the middle; and Ms. Johnson, on the left.
17. THREE PRISONERS
If Prisoner A has a green mark, and Prisoner B has a red mark, then Prisoner C knows he has a red mark; but Prisoner C does not know he has a red mark; and, since Prisoners A and B do not both have green marks, Prisoner A must have a red mark.
18. THREE PRISONERS REVISITED
If A is green and C is red, then B knows.
This is equivalent to saying that if C is red and B does not know, then A is also red.
19. THREE PRISONERS REVISITED AGAIN
Neither A nor B nor C raised his hand. If no one raised his hand, then no one is red. Therefore, A is green.
20. THREE PRISONERS REVISITED ONCE MORE
A knows if B does not know. B knows if A does not know. Neither A nor B knows. Therefore, C is red.
21. THREE PRISONERS REVISITED ONCE MORE AGAIN
A knows and B does not. B knows and A does not. Either A or B knows. Therefore, C is blue.
22. THREE PRISONERS REVISITED ONCE MORE AGAIN EVEN
A knows if B does not know. B knows if A does not know. Either A or B knows. Therefore, C is red.
23. THREE PRISONERS REVISITED EVEN ONCE MORE AGAIN EVEN
A knows and B does not. B knows and A does not. Neither A nor B knows. Therefore, C is green.
24. LOGIC GRADE
If I do well on this assignment, then I will have a better average. If I have a better average, then my grade will be good. However, I'm not doing very well on this assignment. Therefore, my grade will not be very good, or I will do better next time.
25. LOGIC GRADE REVISITED
If I do well on this assignment, then I will have a better average. If I have a better average, then my grade will be good. So far, I'm doing very well on this assignment. Therefore, my grade will be good, or Prisoner C is green.
26. CLIMATE CHANGE
If temperatures rise, earthquakes, hurricanes, and sea levels will also. The last 10 years have seen an increase in earthquakes, hurricanes, and floods. The earth is warming up.
27. TEMPERATURES RISE
If temperatures rise, earthquakes, hurricanes, and sea levels will also. The number of earthquakes and hurricanes has not increased, but coastal cities have been flooded. We cannot conclude then that the earth is warming up.
28. TEMPERATURES RISE HIGHER
If temperatures rise, earthquakes, hurricanes, and sea levels will also. The number of earthquakes and hurricanes has increased, but sea levels have remained constant over the last 30 years. The earth is not warming.
29. FIRE EARTH WIND & WATER
The more fire, the more earth, wind, and water. Therefore, the less earth, the less fire.
30. BLUE STARS
If someone sees a blue star, then either he is immediately enlightened,
or he does not rise to the next level of consciousness.
However, no one is immediately enlightened, but everyone rises to the next level.
Therefore, no one ever sees a blue star.
31. ORANGE STARS
If someone sees a blue star, then either he is immediately enlightened,
or he does not rise to the next level of consciousness.
However, no one is immediately enlightened, but everyone rises to the next level.
Therefore, everyone sees only orange stars.
32. BLUE STARS AGAIN
If someone sees a blue star, then he is immediately enlightened,
and rises to the next level of consciousness.
Somewhere, at some time, someone has seen a blue star.
That someone rose to the next level.
33. ORANGE STARS AGAIN
If everyone sees only orange stars, then they are not immediately enlightened,
but they do rise to the next level of consciousness.
So, if everyone rises to the next level of consciousness,
and, along the way, someone is immediately enlightened,
then that someone sees a blue star.
Hint: Let blue = not orange
Or: Let orange = not blue
34.
If we hurry, then we can be early.
If we can be early, then we can get a better price.
If we can get a better price, then we’ll have money to buy dessert.
Therefore, if we are going to have enough money to buy dessert, we had better hurry.
35.
If the soul is indivisible, then it is indestructible.
If it is indestructible, then it is immortal.
Therefore, if the soul is mortal, then it is divisible.
36. All ethical questions are philosophical questions,
and all philosophical questions are a matter of reasoned judgment.
Thus, no ethical question is a matter of unreasoned judgment.
37.
No cats have wings.
None of my pets have wings.
Therefore, all of my pets are cats.
38.
(1) If it is hot, I will sweat.
(2) If it is cold, I will shiver.
(3) Either it will be hot or cold.
Therefore, either I will sweat or shiver.
39.
(1) If I’m eating chocolate, then I’m happy.
(2) I’m not happy.
(3) If I’m not eating chocolate, then I’ll go crazy.
Therefore, (4) I’ll go crazy.
40.
(1) Either the President will resign or he’ll be kicked out.
(2) The President has no scruples.
(3) If the President has no scruples, then he will not resign.
Therefore, (4) he’ll be kicked out.
41.
(1) If you take your time, then you will be late.
(2) If you show up late, then you will be in trouble.
(3) If you don't take your time, and you still show up late,
you will still be in trouble.
42.
(1) If you take your time, then you will be late.
(2) If you show up late, then you will be in trouble.
(3) You do not get into trouble.
Therefore, (4) you do not take your time.
43.
(1) Either I will drop History or I will drop Math.
(2) If I’m doing well in History, then I will not drop it.
(3) If I’m doing well in Math, then I will not drop it.
Therefore, (4) Either I’m not doing well in History or I’m not doing well in Math.
44.
All humans are mortal.
Some humans are good people.
Therefore, some mortals are good people.
45.
Without an ear, there is no sound.
All forests have ears.
All forests have trees that fall.
So, if a tree falls in the forest, it will make a sound.
Comments:
From wHolt - 2/13/06 10:16 AM
From wHolt - 2/13/06 10:57 AM
HINT #1:
Hilite, copy, and paste this blank table into your comment.
To hilite, press left mouse key and drag mouse across table.
To copy any hilited text, press CTRL+C, or CTRL+INSERT.
To paste, press CTRL+V, or SHIFT+INSERT.
Add and delete columns as necessary.
| A | B | C | |||||||||||||||||
| 0 | 0 | 0 | |||||||||||||||||
| 0 | 0 | 1 | |||||||||||||||||
| 0 | 1 | 0 | |||||||||||||||||
| 0 | 1 | 1 | |||||||||||||||||
| 1 | 0 | 0 | |||||||||||||||||
| 1 | 0 | 1 | |||||||||||||||||
| 1 | 1 | 0 | |||||||||||||||||
| 1 | 1 | 1 |
From wHolt - 2/13/06 11:19 AM
HINT #2:
When making a table, it helps to hit the [insert] key once.
This allows you to overwrite empty spaces without expanding the columns in your table.
HINT #3:
To make this assignment go faster, and reward those who read to the bottom of an assignment,
you do NOT need to make a table if you HoverSnap your output from Brian's Truth Table
and insert it in your comment like this:
Comments:
From wHolt - 12/15/06 5:09 PM
From BassLady - 12/15/06 2:55 PM
I used <=> because the statement starts "If he is a..........then..............."
From wHolt - 12/15/06 10:10 AM
BassLady- (A->C) & (C&B) & <=> B ->C
dont use <=> when you mean NOT.
<=> means if an only if.
Also (A->C) & (C&B) should imply your conclusion.
Notice that your conclusion is also an implication because it has an IF in it.
All of this is simply a matter of substituting the correct symbol for words.
We dont have that many symbols. (ABC + & ~ ->)
Perhaps you are just teasing me?
From wHolt - 12/15/06 10:01 AM
you have not interpreted your statements exactly with your notation.
notice the italicized words and use appropriate symbols:
2. Either Barbie dolls will continue to be favorites, OR Beanie Babies will remain popular.
3. Barbie dolls will NOT continue to be favorites.
4. Then the Bobble head doll craze will NOT continue.
your Statement 1 is right.
From GolfGirl - 12/14/06 4:14 PM
10. BARBIE
If the Bobble head doll craze continues, then Beanie Babies will remain popular. Either Barbie dolls will continue to be favorites, or Beanie Babies will remain popular. Assume Barbie dolls wll not continue to be favorites. Then the Bobble head doll craze will not continue.
A= bobble head doll craze will continue
B= Beanie babies will remain popular
C= Barbie dolls will continue to be favorites
Statement 1:A->B
Statement 2: -C
Statement 3: -c->A
Statement 4: B
INVALID!
From BassLady - 12/14/06 9:06 AM
BassLady - Define your simple statements. That should avoid some confusion.
Like this:
Statement 1 = A = Otis is a disk jockey
Statement 2 = B = Otis knows his history
Statement 3 = C = Otis lives in Lexington
Premise 1: A -> C = If Otis is a disc jockey then he lives in Lexington
[NOTICE THAT YOUR SYMBOLS EXPRESS PREMISE 1 EXACTLY]
B -> C = Otis lives in Lexington AND loves history
[NOTICE THAT YOUR SYMBOLS DO NOT EXPRESS PREMISE 2 EXACTLY]
A = Otis is a history loving disk jockey living in Lexington.
[NOTICE THAT THIS STATEMENT IS NOT THE CONCLUSION,
NOR DOES IT EQUAL SIMPLE STATEMENT A]
Conclusion: If he were not a history buff then he would not be a disk jockey.
[NOTATE THIS SENTENCE EXACTLY USING LETTERS WITH PROPER OPERATORS]
If Otis is a disc jockey then he lives in Lexington - (A ->C)
Otis lives in Lexington AND loves history - (C & B)
Conclusion - If he were not a history buff then he would not be a disk jockey. (<=> B->C)
Is this closer to what I should be? (A->C) & (C&B) & <=> B ->C
From wHolt - 12/7/06 11:05 AM
Bubba - I wont list all the errors, but here is the first one:
Notice that in A knows if B does not, the IF is in front of the B.
You got the implication backwards.
The statement is equal to If B does not know, then A knows.
From Bubba - 12/6/06 10:31 AM
three prisoners revisited again
a knows if b does not.
b knows if a does not.
neither a nor b knows.
therefore c is red.
A : a knows
B: b knows
C: neither knows
conclusion is D: c is red
((A => ~B) & (B => ~A)) => -C
From wHolt - 11/30/06 9:51 AM
BassLady - Define your simple statements. That should avoid some confusion.
Like this:
Statement 1 = A = Otis is a disk jockey
Statement 2 = B = Otis knows his history
Statement 3 = C = Otis lives in Lexington
Premise 1: A -> C = If Otis is a disc jockey then he lives in Lexington
[NOTICE THAT YOUR SYMBOLS EXPRESS PREMISE 1 EXACTLY]
B -> C = Otis lives in Lexington AND loves history
[NOTICE THAT YOUR SYMBOLS DO NOT EXPRESS PREMISE 2 EXACTLY]
A = Otis is a history loving disk jockey living in Lexington.
[NOTICE THAT THIS STATEMENT IS NOT THE CONCLUSION,
NOR DOES IT EQUAL SIMPLE STATEMENT A]
Conclusion: If he were not a history buff then he would not be a disk jockey.
[NOTATE THIS SENTENCE EXACTLY USING LETTERS WITH PROPER OPERATORS]
From BassLady - 11/29/06 7:43 PM
Okay let's give it another go. I know how to do this, but I just can't seem to put in the correct symbols.
#13 - If Otis is a disc jockey, then he lives in Lexington. He does live in Lexington, and, furthermore, he is a history buff. So, if Otis were not a history buff, he would not be a disc jockey either?
Premise 1: If Otis is a disk jockey, then he lives in Lexington.
Premise 2: He does live in Lexington, and furthermore he is a history buff.
Conclusion: If he were not a history buff then he would not be a disk jockey either.
Statement 1 - Otis is a disk jockey
Statement 2 - Otis knows his history
Statement 3 - Otis lives in Lexington
| A | B | C | (A->C) | & | (B->C) | ->A |
| 0 | 0 | 0 | 1 | 1 | 1 | 0 |
| 0 | 0 | 1 | 1 | 1 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 | 0 | 1 |
| 0 | 1 | 1 | 1 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
A -> C = If Otis is a disc jockey then he lives in Lexington
B -> C = Otis lives in Lexington and loves history
A = Otis is a history loving disk jockey living in Lexington.
From wHolt - 11/23/06 10:45 AM
#13 - Slipped Disc -
PREMISE 1: If Otis is a disk jockey, then he lives in Lexington.
PREMISE 2: He does live in Lexington, and furthermore, he is a history buff.
CONCLUSION: So, if Otis were not a history buss, he would not be a disc jockey either?
Statement #1 - A=Otis is a disk jockey
Statement #2 - B=Otis know history
Statement #3 - C=Otis lives in Lexington
(PREMISE 1 & PREMISE 1) => CONCLUSION
I commented on this one quite a bit above.
Dont use <=> for =>.
All you need to do is sub in A B C with the appropriate operators & ~ + ->
and you have it...
From BassLady - 11/22/06 11:20 PM
Okay, I need help. If Otis is a disc jockey, then he lives in Lexington. He does live in Lexington, and, furthermore, he is a history buff. So if Otis were not a history buff, he would not be a disc jockey either?
You have a question mark at the end of the sentence. Do I have a choice here. If I do ----then I choose he is a disc jockey who lives in Lexington loving the history channel. Am I on the right track????
Premise A - Otis is a disc jockey
Premise B - Otis lives in Lexington
Premise C - Otis loves history
Conclusion - Otis is a history loving disc jockey living in Lexington.
(A->B) & (B->C) & (C <=> A) = A
Please help me.
From wHolt - 11/20/06 12:21 PM
I dont know why you put 2 negatives in your concluding statement: -(A=>-C)
If it is an ethical question, then it is not a case of unreasoned judgment = (A=>-C)
This says the same thing as the conclusion.
From Zonino - 11/19/06 9:12 PM
36. All ethical questions are philosophical questions,
and all philosophical questions are a matter of reasoned judgment.
Thus, no ethical question is a matter of unreasoned judgment.
1. Ethical questions are philosophical questions.
2. Philosophical questions are a matter of reasoned judgment.
3. No ethical question is a matter of unreasoned judgment.
A = There are ethical questions.
B = There are philosophical questions.
C = There are questions that are matters of reasoned judgment.
Statement 1 A => B
Statement 2 B => C
Statement 3 –(A => –C)
(A=>B)&(B=>C)=>-(A=>-C)
The arguement is invalid.
From DirtyBird - 10/22/06 10:00 AM
If that tree is infested with pine bark beetles, then it will die. People plant trees on Arbor Day and it will not die. Therefore, if people plant trees on Arbor Day, then that tree is not infested with pine bark beetles.
A= Pine bark beetles kill trees
B= People plant trees on Arbor Day.
C= Trees are infested with pine bark beetles.
Statement 1= C=>A
Statement 2= B&~A
Statement 3= B=>~C
VALID
From wHolt - 10/19/06 12:58 AM
Future Lawyers of America:
Boki
CatsEyes
Cheana
DirtyBird
Draco
Fro
Harkar
Houdini
JooJoo
Kathi
Lexiowen
Pac
Pod
Poovey
Pringle
Slick
Sunshine
SuperDuke
From wHolt - 10/19/06 12:56 AM
DirtyBird-
someohow Statement 2= B&~A did not make it into Brians applet
BassLady- i need new reading glasses
i dont see any changes
Poovey - have another chocolate!
From Poovey - 10/18/06 8:58 PM
2) I'm not happy
3) If I'm not eating chocolate, then I'll go crazy
Therefore, 4) I'll go crazy
a) I'm eating chocolate
b) I'm happy
c) I'll go crazy
1. A=>B
2. -B
3. -A=>C
conclusion=c
it is valid..............
From BassLady - 10/18/06 8:34 PM
#13 - If Otis is a disk jockey, then he lives in Lexington. He does live in Lexington, and furthermore, he is a history buff. So if Otis were not a history buff, he would not be a disk jockey either.
| A | B | C | (A<=>B) | & | (A <=> C) | & | (B <=> C) |
| 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
| 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
A = If Otis is a disk jockey, he lives in Lexington.
B = If Otis is a disk jockey, he is also a history buff.
C = Otis is a disk jockey, history loving man living in Lexington.
This table is a conditional table
From wHolt - 10/18/06 11:43 AM
Poovey-
1) If I'm eating chocolate, then I'm happy
2) I'm not happy
3) If I'm not eating chocolate, then I'll go crazy
Therefore, 4) I'll go crazy
a) I'm eating chocolate
b) I'm not happy [THIS IS NOT SIMPLE. IT HAS A NOT IN IT!]
c) I'll go crazy
1. A=>B
2. -A=>-B [THERE IS NO IMPLICATION IN PREMISE 2]
3. -A=>C
conclusion=c
Dirty Bird-
People plant trees on Arbor Day AND it will not die.
[PREMISE 2 IS NOT AN IMPLICATION. Fix]
BassLady-
If Otis is a disk jockey, then he lives in Lexington.
[THERE ARE NO IF AND ONLY IFS IN YOUR ARGUMENT]
He does live in Lexington, and furthermore, he is a history buff.
[THERE IS NO IMPLICATION IN PREMISE 2]
So if Otis were not a history buff, he would not be a disk jockey either.
[PREMISE 1 AND 2 MUST IMPLY THE CONCLUSION. THERE IS A NOT IN IT. FIX.]
A - Otis is a disk jockey
B - Otis lives in Lexington
C - Otis is a history buff
((A<=>B) & (B<=>C) & (A<=>C)
From BassLady - 10/17/06 11:20 PM
#13 - If Otis is a disk jockey, then he lives in Lexington. He does live in Lexington, and furthermore, he is a history buff. So if Otis were not a history buff, he would not be a disk jockey either.
A - Otis is a disk jockey
B - Otis lives in Lexington
C - Otis is a history buff
| A | B | C | ((A<=>B) | & | (B<=>C) | & | (A<=>C) |
| 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
| 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
| 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
From Poovey - 10/17/06 6:49 PM
From wHolt - 10/17/06 2:35 PM
DirtyBird - match your notation with your argument.
If that tree is infested with pine bark beetles, then it will die. (this not B=>~C)
People plant trees on Arbor Day and it will not die. (this not C=>A)
Therefore, if people plant trees on Arbor Day, then that tree is not infested with pine bark beetles. (This is not B=>~A)
A= Pine bark beetles kill trees
B= People plant trees on Arbor Day.
C= Trees are infested with pine bark beetles.
Statement 1= B=>~C
Statement 2= C=>A
Statement 3= B=>~A
I will ignore your next attempt if you ignore these remarks.
Poovey - copy your argument so we can tell what you are doing.
From Poovey - 10/16/06 5:15 PM
1) If I'm eating chocolate, then I'm happy
2) I'm not happy
3) If I'm not eating chocolate, then I'll go crazy
Therefore, 4) I'll go crazy
a) I'm eating chocolate
b) I'm not happy
c) I'll go crazy
1. A=>B
2. -A=>-B
3. -A=>C
conclusion=c
From wHolt - 10/16/06 2:20 PM
Future Lawyers of America:
Boki
CatsEyes
Cheana
Draco
Fro
Harkar
Houdini
JooJoo
Kathi
Lexiowen
Pac
Pod
Pringle
Slick
Sunshine
SuperDuke
From wHolt - 10/16/06 2:18 PM
DirtyBird-
These notations do not match your argument:
Statement 1= A=>B
Statement 2= B=>c
Statement 3= C=>B
Conclusion= A
Compare them to the argument.
There are only 3 sentences in the argument.
Zonino-
(~A=>~C) says "if it is not an ethical question then it is unreasonable."
try ~(A=>~C) = "it is never true that if it is ethical then it is unreasonable."
or does it say "if it is ethical then it is not unreasonalbe"?
From CatsEyes - 10/16/06 8:50 AM
4. FLU
If you catch the flu, you can infect others. Sore throats, however, cannot infect others. But, if sore throats could infect others, you would definitely catch the flu.
A=You catch the flu
B=Can Infect others
C=Sore throats
Statement 1 = A => B
Statement 2 = C => ~B
Conclusion = (C => B) => A
Argument is invalid.
From Kathi - 10/16/06 8:02 AM
1. COUNTRY SONG
If you wuz my woman, an' I wuz yer man, I'd never stop lovin you.But, darlin, I've stopped lovin you. So, you ain't my woman, or I ain't yer man.
- If I am your man and you are my woman, I love you.
- I don't love you.
- You are not my woman or I am not your man
Let A = You are my woman
Let B = I am your man .
Let C = I love you.
Statement 1 is expressed as (A & B) => C
Statement 2 is expressed as –C
Conclusion is expressed as (-A + -B)
(((A & B) => C) & ~C) => (~A + ~B)
This argument is valid.
From Zonino - 10/15/06 10:13 PM
and all philosophical questions are a matter of reasoned judgment.
Thus, no ethical question is a matter of unreasoned judgment.
1. Ethical questions are philosophical questions.
2. Philosophical questions are a matter of reasoned judgment.
3. No ethical question is a matter of unreasoned judgment.
A = There are ethical questions.B = There are philosophical questions.
C = There are questions that are matters of reasoned judgment.
Statement 1 A -> B
Statement 2 B -> C
Statement 3 –A -> –C
(A -> B) & (B -> C) -> (-A -> –C)
The arguement is not valid.
From Draco - 10/15/06 6:01 PM
29. FIRE EARTH WIND & WATER
The more fire, the more earth, wind, and water. Therefore, the less earth, the less fire.
Statement 1: The more fire, the more earth. (A->B)
Statement 2: The more fire, the more wind. (A->C)
Statement 3: The more fire, the more water. (A->D)
Statement 4: The less earth, the less fire.(-B->-A)
A= More fire.
B= More earth.
C= More wind.
D= More water.
Compound Statement: [(A->B)&(A->C)&(A->D)]->(-B->-A)
ARGUMENT IS VALID
From DirtyBird - 10/15/06 1:55 PM
9. BEETLES
If that tree is infested with pine bark beetles, then it will die. People plant trees on Arbor Day and it will not die. Therefore, if people plant trees on Arbor Day, then that tree is not infested with pine bark beetles.
A= Pine bark beetles kill trees
B= People plant trees on Arbor Day.
C= Trees are infested with pine bark beetles.
Statement 1= B=>~C
Statement 2= C=>A
Statement 3= B=>~A
Argument is VALID
I dont know what Im doing wrong on my notation.
From wHolt - 10/15/06 1:39 PM
CatsEyes - this <=> means if and only if.
there are none in your argument. Fix.
DirtyBird-
your notation does not fit this statement:
If that tree is infested with pine bark beetles, then it will die.
(this is an IF)
and fix these also:
Statement 1= ~(B<=>A)
Statement 2= B->c
Statement 3= -C
From CatsEyes - 10/14/06 7:16 PM
4. FLU
If you catch the flu, you can infect others. Sore throats, however, cannot infect others. But, if sore throats could infect others, you would definitely catch the flu.
A=You catch the flu
B=Can Infect others
C=Sore throats
Statement 1 = A => B
Statement 2 = C <=> ~B
Conclusion = (C <=> B) => A
Argument is invalid.
(I hope this is correct this time)
From wHolt - 10/14/06 2:54 PM
BassLady
if
A= Otis is a disk jockey
B= Otis know history
C= Otis lives in Lexington
then your premises were not notated correctly.
Phoenix-
this is the conclusion:
"If you don't take your time, and you still show up late,
you will still be in trouble."
this not ~A.
From Phoenix - 10/14/06 1:23 AM
41.
(1) If you take your time, then you will be late.
(2) If you show up late, then you will be in trouble.
(3) If you don't take your time, and you still show up late,
you will still be in trouble.
A= You take your time
B= You will be late
C= You will be in trouble
Statement 1: A->B
Statement 2: B->C
Conclusion: ~A
Arguement is invalid
From BassLady - 10/13/06 9:04 PM
From BassLady - 10/12/06 7:47 PM
| A | B | C | ((A => B) | & | (B => C) | & | -C | => | -A | ||||||||||
| 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ||||||||||
| 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | ||||||||||
| 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | ||||||||||
| 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | ||||||||||
| 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | ||||||||||
| 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | ||||||||||
| 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | ||||||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 |
#13 - Slipped Disc - If Otis is a disk jockey, then he lives in Lexington. He does live in Lexington, and furthermore, he is a history buff. So, if Otis were not a history buss, he would not be a disc jockey either?
Statement #1 - Otis is a disk jockey
Statement #2 - Otis know history
Statement #3 - Otis lives in Lexington
If Otis is a disk jockey, he lives in Lexington. He is a history buff. this argument is valid.
From wHolt - 10/13/06 2:40 PM
THIS EXERCISE IN MADNESS IS NOW CLOSED TO NEWCOMERS!
YOU 13 OLDCOMERS CONTINUE ARGUING.
YOU ARE NOT FAR FROM YOUR 7 POINTS!
From wHolt - 10/13/06 2:38 PM
CatsEyes-simple statements good.
"Sore throats, however, cannot infect others." is an implication. fix
"But, if sore throats could infect others, you would definitely catch the flu."
is the conclusion and contains all three simple statements somehow.
Zonino - there is no if and only if <=> in your argument. fix.
Also simple statements would be simpler as
A = there are ethical Questions
B = there are philosophical Questions.
C = there are Questions that are a matter of reasoned judgment.
However, close enough for the extra point.
DirtyBird -
If that tree is infested with pine bark beetles, then it will die. (your notation says they will live)
People plant trees on Arbor Day AND it will not die. (there is no IF in this one)
Therefore, if people plant trees on Arbor Day, then that tree is not infested with pine bark beetles.
(there is an IF in this one)
your simple statements are:
A= Pine bark Beetles kill trees
B= People plant trees on Arbor Day.
C= Trees are infested with pine bark beetles.
go forth and conquer...
From wHolt - 10/13/06 2:37 PM
Future Lawyers of America:
Boki
Cheana
Fro
Harkar
Houdini
JooJoo
Lexiowen
Pac
Pod
Pringle
Slick
Sunshine
SuperDuke
From Lexiowen - 10/12/06 10:01 PM
24. LOGIC GRADE
If I do well on this assignment, then I will have a better average. If I have a better average, then my grade will be good. However, I'm not doing very well on this assignment. Therefore, my grade will not be very good, or I will do better next time.
A: I'll do well on this assignment.
B: I will have abetter average.
C: My grade will be good.
D: I will do better next time.
Statement 1: A->B
Statement 2: B->C
Statement 3: -A
Statement 4: -C+D
valid
From Zonino - 10/12/06 9:58 PM
36. All ethical questions are philosophical questions,
and all philosophical questions are a matter of reasoned judgment.
Thus, no ethical question is a matter of unreasoned judgment.
- Ethical questions are philosophical questions.
- Philosophical questions are a matter of reasoned judgment.
- No ethical question is a matter of unreasoned judgment.
A = Questions are ethical.
B = Questions are philosophical.
C = Questions are a matter of reasoned judgment.
Statement 1 A <=> B
Statement 2 B <=> C
Statement 3 –A <=> –C
(A <=> B) & (B <=> C) -> (-A <=> –C)
Arguement is valid.
From CatsEyes - 10/12/06 9:51 PM
4. FLU
If you catch the flu, you can infect others. Sore throats, however, cannot infect others. But, if sore throats could infect others, you would definitely catch the flu.
A=You catch the flu
B=Can Infect others
C=Sore throats
Statement 1 = A => B
Statement 2 = C & ~B
Statement 3 = C => B
Conclusion = A
This argument is valid.
From wHolt - 10/12/06 9:12 PM
TBird - there are no if and only ifs in your argument.
Simple statements are good though.
DirtyBird - you put negations in your simple statements. Fix.
BassLady - you did not copy your argument.
So how can we tell if you translated OK?
Put your notation next to each statement.
Bubba - your C contains a negative.
What happened to a simple statement with RED in it?
You dont need a D.
Phoenix - there are only 3 statements in the argument.
Dont make it 4.
From Phoenix - 10/12/06 9:01 PM
41.
(1) If you take your time, then you will be late.
(2) If you show up late, then you will be in trouble.
(3) If you don't take your time, and you still show up late,
you will still be in trouble.
A= You take your time
B= You will be late
C= You will be in trouble
Statement 1: A->B
Statement 2: B->C
Statement 3: B
Conclusion: ~A
Arguement is invalid
From Bubba - 10/12/06 8:38 PM
three prisoners revisited again
a knows if b does not.
b knows if a does not.
neither a nor b knows.
therefore c is red.
A : a knows
B: b knows
C: neither knows
conclusion is D: c is red
((A => ~B) & (B => ~A) => C) => D
this statement is invalid
From BassLady - 10/12/06 7:47 PM
| A | B | C | ((A => B) | & | (B => C) | & | -C | => | -A | ||||||||||
| 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ||||||||||
| 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | ||||||||||
| 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | ||||||||||
| 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | ||||||||||
| 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | ||||||||||
| 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | ||||||||||
| 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | ||||||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 |
#13 - Slipped Disc
Statement #1 - Otis is a disk jockey
Statement #2 - Otis know history
Statement #3 - Otis lives in Lexington
If Otis is a disk jockey, he lives in Lexington. He is a history buff even if he is not a disk jockey.
From wHolt - 10/12/06 6:46 PM
Draco - Pac already worked your selection. Pick another.
7Iron - Notate means symbolize the notation to match the sentences in the argument.
Phoenix- simple statements good, but not your conclusion:
"If you don't take your time, and you still show up late,
you will still be in trouble."
Fix your notation.
Golfgirl- hilite and copy your original argument, or we cant tell what you are doing.
From Draco - 10/12/06 5:25 PM
6. RUNNING
If Hillary runs, McCain will not. But Hillary will run if Bill tells her to. McCain decides to run. So Bill did not tell Hillary to run.
Statement 1: If Hillary runs, McCain will not.
Statement 2: Hillary will run if Bill tells her to.
Statement 3: McCain decides to run.
Statement 4: Bill did not tell Hillary to run.
A=Hillary runs.
B=McCain runs.
C=Bill tells Hillary to run.
Statement 1= A -> -B
Statement 2= C -> A
Statement 3= B
Statement 4= -C
Compound Statement= [ (A -> -B) & (C-> A) & B] -> -C
Argument is valid.
From 7Iron - 10/12/06 5:21 PM
Mr Holt,
I do not understand what you mean by notate??
7IRON
From Phoenix - 10/12/06 2:05 AM
41.
(1) If you take your time, then you will be late.
(2) If you show up late, then you will be in trouble.
(3) If you don't take your time, and you still show up late,
you will still be in trouble.
A= You take your time
B= You will be late
C= You will be in trouble
Statement 1: A->B
Statement 2: B->C
Statement 3: B
Conclusion: C
Arguement is valid
From GolfGirl - 10/12/06 12:56 AM
10. BARBIE
If the Bobble head doll craze continues, then Beanie Babies will remain popular. Either Barbie dolls will continue to be favorites, or Beanie Babies will remain popular. Assume Barbie dolls wll not continue to be favorites. Then the Bobble head doll craze will not continue.
A= bobble head dollg craze will continue
B= Beanie babies will remain popular
C= Barbie dolls will not continue to be favorites
Statement 1:A+B
Statement 2: -C
Statement 3: -c->A
Statement 4: B
INVALID!
From JooJoo - 10/11/06 10:29 PM
#39
1) If I'm eating chocolate, then I'm happy
2) I'm not happy
3) If I'm not eating chocolate, then I'll go crazy
Therefore, 4) I'll go crazy
A. I'm eating chocolate
B. I'm happy
C. I'll go crazy
1. A->B
2. -B
3. -A -> C
4. C
(A->B) & (-B) & (-A->C) -> C
From Poovey - 10/11/06 9:06 PM
@@##$$%%
I must have been working on the same thing while JooJoo was!
From JooJoo - 10/11/06 8:42 PM
I would like to claim # 39 but I am at work right now so I will finish the rest of the table when I get home.
#39
1) If I'm eating chocolate, then I'm happy
2) I'm not happy
3) If I'm not eating chocolate, then I'll go crazy
Therefore, 4) I'll go crazy
A. I'm eating chocolate
B. I'm happy
C. I'll go crazy
1. A->B
2. -B
3. -A -> C
4. C
[(A->B) & (-B) & (-A->C)] -> C
(Sorry I will finish with the Hoversnap picture when I get home)
From Fro - 10/11/06 8:34 PM
43.
(1) Either I will drop History or I will drop Math.
(2) If I’m doing well in History, then I will not drop it.
(3) If I’m doing well in Math, then I will not drop it.
Therefore, (4) Either I’m not doing well in History or I’m not doing well in Math.
A=I will drop Math
B=I will drop History
C=I'm doing well in History
D=I am doing well in Math
Statement 1: A+B
Statement 2: C=>-A
Statement 3: D=>-B
Statement 4: -C+-D
Argument is valid
From Pringle - 10/11/06 8:32 PM
11. AMERICAN IDOL
1) Christina Aguilera sings tonite, or Ricky Martin is no longer a teen idol.
2) If Ricky Martin is not a teen idol anymore, then Britney Spears will not win an American Music Award.
3) But Britney Spears does win an American Music Award.
4) Therefore, Christina Aguilera does not sing tonite.
let A = Christina Aguilera sings tonite.
let B = Ricky Martin is a teen idol.
let C = Britiney Spears wins an Americal Idol.
Statement 1 = A + -B
Statement 2 = -B -> -C
Statement 3 = C
Conclusion = -A
[(A + -B) & (-B -> -C) & C] => -A
This is invalid!
From TBird - 10/11/06 8:02 PM
38.
(1) If it is hot, I will sweat.
(2) If it is cold, I will shiver.
(3) Either it will be hot or cold.
Therefore, either I will sweat or shiver.
A= its hot
B= I will sweat
C= its cold
D= I will shiver
This argument is a valid one becuase if its hot then i will sweat and if its cold i will shiver...enless im really sick with a fever
From wHolt - 10/11/06 12:05 PM
7Iron - notate these statements
(1.) All humans are mortal.
(2.) Some humans are good people.
(3.) Therefore, some mortals are good people.
DirtyBird- you will need a D statement for yours.
A= We hurry.
B= We can be early.
C= Can get a better price.
D= Extra money for dessert.
Kathi- you were closer before.
Notate these statements:
If you wuz my woman, an' I wuz yer man, I'd never stop lovin you. (note the IF an' AND)
But, darlin, I've stopped lovin you.
So, you ain't my woman, or I ain't yer man. (note the OR in the conclusion)
From Kathi - 10/11/06 11:37 AM
1. COUNTRY SONG
If you wuz my woman, an' I wuz yer man, I'd never stop lovin you.But, darlin, I've stopped lovin you. So, you ain't my woman, or I ain't yer man.
Let A = You are my woman.
Let B = I am your man .
Let C = I love you.
Statement 1 is expressed as A AND B
Statement 2 is expressed as C AND B
Statement 3 is expressed as –C
[(A & B) & (C & B) & —C] -> —A + -B
This argument is valid.
From 7Iron - 10/10/06 5:18 PM
(1.) All humans are mortal.
(2.) Some humans are good people.
(3.) Therefore, some mortals are good people.
A= They are human.
B= They are mortal.
C= They are good people.
Statement1= A
Statement2= B
Conclusion= C
Not Valid
From wHolt - 10/10/06 11:04 AM
Future Lawyers of America:
Boki
Cheana
Harkar
Houdini
Pac
Pod
Slick
Sunshine
SuperDuke
From wHolt - 10/10/06 11:02 AM
Dirtybird- you should also have a simple statement for "We hurry". Redo.
Pod - you have a typo in (C -> -A) & (B -> -A) = (B -> C). dont use = sign. use =>
they mean something different. the = means <=> in logic.
7Iron- your simple statements are:
A= they are human
B= they are mortal
C= they are good people
try again
Hotrod- simple statements are good.
But you did not follow the 3 statements of the argument
1. All work and no play made Jack a dull boy.
2. However, since his recent layoff from work, Jack has been playing around a lot.
3. At least he's not dull anymore.
Make your symbols accord with these 3 statements.
Pac- you made the list. Congrats!
From HotrodMinivan - 10/10/06 9:46 AM
#3. Jack
All work and no play made Jack a dull boy. However, since his recent layoff from work, Jack has been playing around a lot. At least he's not dull anymore. Let W=Jack works, P=Jack plays, and D=Jack is dull.
W=Jack works P=Jack plays D=Jack is dull
Statement 1: W=>DStatement 2: P=>-DStatement 3: DConclusion: -W^ P => -D
This arguement is valid. If Jack works and does not play, he is dull. However if he does not work he does not eat, but he is not dull. To correct this he needs to let work and play balance each other.
From Pac - 10/9/06 8:26 PM
6. RUNNING
If Hillary runs, McCain will not. But Hillary will run if Bill tells her to. McCain decides to run. So Bill did not tell Hillary to run.
1. If Hillary runs, McCain will not.
2. Hillary will run if Bill tells her to.
3. McCain decides to run.
Conclusion: Bill did not tell Hillary to run.
Statements:
H = Hillary runs
B = Bill tells Hillary to run
M = McCain runs
Breakdown:
Statement 1: H -> -M
Statement 2: B -> H
Statement 3: M
Conclusion: -B
Argument string: ((H -> -M) & (B -> H) & M) -> -B
Identity - VALID! :-)
From Pod - 10/9/06 6:51 PM
37.
No cats have wings.
None of my pets have wings.
Therefore, all of my pets are cats.
A = It has wings
B = It is my pet.
C = It is a cat.
Statement 1: C -> -A
Statement 2: B -> -A
Conclusion: B = C
(C -> -A) & (B -> -A) = (B -> C)
invalid.
From wHolt - 10/9/06 2:14 PM
Kathi - there is no if and only if in the argument.
also, notice the concluding sentence is compound.
Pod -
Your simple statements should be:
A=It has wings.
B=It is my pet.
C=It is a cat.
Melewen- simple statements are good.
But the conclusion is not an if and only if.
Just a simple if. Fix.
Superduke- I will give you credit.
Although "All forests have ears"
means "if it is a forest, then it has ears."
Harkar - 8 points!
From Sunshine - 10/9/06 10:41 AM
8. GOLF
Jeff loves to play golf. If Joan likes to sew, then Jeff does not love to play golf. If Joan does not like to sew, then Brad sings in the choir. Therefore, Brad sings in the choir.
A: Jeff lives to play golf.
B: Joan likes to sew.
C: Brad sings in the choir.
From Kathi - 10/9/06 7:47 AM
1. COUNTRY SONG
If you wuz my woman, an' I wuz yer man, I'd never stop lovin you.But, darlin, I've stopped lovin you. So, you ain't my woman, or I ain't yer man.
Let A = You are my woman.
Let B = I am your man .
Let C = I love you.
Statement 1 is expressed as A <-> B
Statement 2 is expressed as C AND B
Statement 3 is expressed as -C
[(A <=> B) & (C & B) & —C] -> —A
This argument is valid.
From Pod - 10/8/06 9:28 PM
37.
No cats have wings.
None of my pets have wings.
Therefore, all of my pets are cats.
A = Cats have wings
B = My pets have wings
C = All my pets are cats.
Statement 1: -A
Statement 2: -B
Conclusion: C
(-A & -B) -> C
invalid.
From Melewen - 10/8/06 9:25 PM
If we hurry, then we can be early.
If we can be early, then we can get a better price.
If we can get a better price, then we’ll have money to buy dessert.
Therefore, if we are going to have enough money to buy dessert, we had better hurry.
Let A = We hurry.
Let B = We can be early.
Let C = We can get a better price.
Let D = We'll have enough money for dessert.
Statement 1 = A -> B
Statement 2 = B -> C
Statement 3 = C -> D
Conclusion = D <=> A
[((A -> B) & ((B -> C) & (C -> D))) -> (D <=>A)]
INVALID! Conditional statement.
From SuperDuke - 10/8/06 6:13 PM
#45 Without an ear, there is no sound. All forest have ears. All forest have trees that fall. So if a tree falls in the forest, it will make a sound.
A. There is a sound.
B. Forest have ears.
C. Forest trees fall.
1. ~B => ~A
2. B
3. C
Conc: C => A
Argument is invalid
From Harkar - 10/8/06 5:41 PM
#40
(1) Either the President will resign or he will be kicked out.
(2) The President has no scruples.
(3) If the President has no scruples, then he will not resign.
Therefore, (4) he'll be kicked out.
A= The President will resign.
B= The President will be kicked out.
C= The President has scruples.
Statement 1 = A+B
Statement 2 = -C
Statement 3 = -C => -A
Conclusion = B
| A | B | C | ((A+B) | & | -C | & | (-C | =>A)) | => B | |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | |
| 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | |
| 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | |
| 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | |
| 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | |
| 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
| 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 |
This argument is invalid.
From wHolt - 10/8/06 12:28 AM
Cheana - nice example. Thanks.
7Iron - your statements 2 and 3 are nowhere in the argument.
For this argument to make any sense, A=C.
Therefore there are actually only two simple statements that comprise this argument.
From Cheana - 10/7/06 12:50 PM
2. MISS AMERICA
Either Miss Pennsylvania wins the Miss America Pageant, or Miss Kentucky is first runner up, but not both. However, Miss Kentucky is first runner up if and only if Miss Rhode Island is the second runner up. But Miss Rhode Island is not the second runner up. Therefore, Miss Pennsylvania is not Miss America.
A= Miss Pennsylvania wins the Miss America Pageant.
B= Miss Kentucky is first runner up.
C= Miss Rhode Island is second runner up.
Statements:
1= A XOR B (A %B)
2= B EQV C (B <=> C)
3= NOT C (~C)
Conclusion= NOT A (~A)
Argument is Invalid
From wHolt - 10/5/06 12:47 AM
Boki - Good job. Although indestructible, indivisible, and immortal are all 3 negatives.
Sunshine & Everyone - put a copy of your argument in the comment so we know what you are doing!
From Slick - 10/4/06 9:11 PM
#42 If you take your time, then you will be late.
If you show up late, then you will be in trouble.
You do not get in trouble. Therefore, you do not take your time.
A = You take your time
B = You will be late
C = You will be in trouble
Statement 1: A->B
Statement 2: B->C
Statement 3: -C
Conclusion: -A
This Argument is valid
From Sunshine - 10/4/06 2:03 PM
#8
A: Jeff lives to play golf.
B: Joan likes to sew.
C: Brad sings in the choir.
From Boki - 10/4/06 12:23 PM
If the soul is indivisible, then it is indestructible.
If it is indestructible, then it is immortal.
Therefore, if the soul is mortal, then it is divisible.
A= The soul is indivisible.
B= It is indestructible.
C= It is immortal.
Statement 1 = A -> B
Statement 2 = B-> C
Statement 3 = ~CConclusion = ~A
The argument is valid.
(( A -> B) & (B -> C) & ~C) -> ~A
“The soul never thinks without a picture.” – Aristotle
From wHolt - 10/2/06 12:57 PM
Houdini did it!
Everyone study Houdini's before you do yours!
From Houdini - 10/2/06 9:52 AM
14. BANK
If I write a check it will bounce. If the bank guarantees it, then it will not bounce. The bank will guarantee alright. So I don't write the check.
A=I write a check
B=The bank guarantees it.
C=It will bounce.
Statement 1 = A→C
Statement 2 = B→-C
Statement 3 = B
Conclusion = -A
This argument is valid. Even though the bank will guarantee the check so it will not bounce, the bank will charge you an arm and a leg, maybe even a pound of flesh, to cover the check. To save me from this, I will not write the check and buy Disney's Alice in Wonderland next paycheck.
From wHolt - 9/29/06 1:20 PM
Kathi- nice of you to go first.
here are your simple statements:
Let A = You are my woman.
Let B = I am your man .
Let C = I love you.
There are only 3 sentences in the argument:
two premises and one conclusion.
Dont make it 4.
Also there is no if and only if implied anywhere.
Just use IF.
To make it easy, Hoversnap your argument in Brian's Truth Constructor.
Then insert it in a comment.
Go =>
From Kathi - 9/29/06 10:30 AM
1. COUNTRY SONG
If you wuz my woman, an' I wuz yer man, I'd never stop lovin you.But, darlin, I've stopped lovin you. So, you ain't my woman, or I ain't yer man.
- I will never stop loving you if I am your man and you are my woman.
- Either I love you or I am not your man and you are not my woman
- I stopped loving you.
Let A = You are my woman.
Let B = I am your man .
Let C = I love you.
Statement 1 is expressed as A <-> B
Statement 2 is expressed as C AND B
Statement 3 is expressed as -C
[(A <=> B) & (C & B) & —C] -> —A
This argument is valid.
Last Modified 9/29/06 1:40 PM
EXAMPLE: FOOTBALL PLAYOFFS
Make the truth table for the argument below:
STATEMENTS
1. The Colts will be in the playoffs if and only if Peyton leads the league in passing.
2. Either Marv loves the Colts, or Peyton leads the league in passing, but not both.
3. Marv does not love the Colts.
4. Therefore, the Colts will not be in the playoffs.
First, identify the simple statements in this argument:
Let A = the Colts will be in the playoffs.
Let B = Peyton leads the league in passing.
Let C = Marv loves the Colts.
Next write each sentence as a compound statement:
Statement 1 is expressed in symbols as A <=> B.
Statement 2 becomes C Å B. (The Å is the EXCLUSIVE OR or XOR.)
Statement 3 is simply —C.
Statement 4 is —A.
Now conjunct all but the last of these statements together in a long compound statement;
and then connect the last statement at the end with an implication.
[(A EQV B) AND (C XOR B) AND NOT C] IMP (NOT A)
Use Brian's Truth Constructor.
Then copy the results into a table:
ARGUMENT INVALID