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Validity |
Brian's Applet
TYPES OF ARGUMENTS
A valid argument is one that is always true
regardless of the truth of the premises and their conclusion.
In other words, a valid argument uses logical reasoning;
but an invalid argument uses faulty reasoning.
We use truth tables to distinguish between valid and invalid arguments.
We test the validity of an argument by following these steps:
- Write each argument as two premises and one conclusion.
- Break down the argument into simple statements (no NOTs, ANDs, or ORs).
- Convert premises and conclusion into symbols.
- Conjoin premises together (AND them).
- Do the conjoined premises imply the conclusion on all 4 rows?
Use the A–>B table above to determine if all 4 rows are 1's. - If yes, argument is valid; else invalid, even if only one row is false.
We can also test the validity of arguments using diagrams.
As we did before with our sets diagrams,
a logic diagram uses circles to represent simple statements.
Notice that in each of the examples below, the conditional arrow ®, for implies,
is interpreted visually as one circle inside another.
A®B means that if something—call it x—is in circle A, then it is also in circle B.
The circle A means that some x is in A; circle B means some x is in circle B.
Whereas, –A means outside A, and –B means outside B.
The x shows us where the truth is and where the conclusion belongs.
Sometimes x overlaps a boundary, because some of the things in x are inside a circle,
and some of the other things in x are outside the circle.
These diagrams were invented by Leonard Euler more than 200 years ago.
Here are some links that explain more about Euler's diagrams.
Below are examples of 6 forms of argument and their corresponding diagrams.
1. DIRECT REASONING
If Anne passes finite math, then Bill passes finite math.
Anne passes.
So Bill passes too.
A = Anne passes finite math.
B = Bill passes finite math.
Premise 1: A -> B (If Anne passes, then Bill passes.)
Premise 2: A (Anne passes.)
Conclusion: B (Bill passes.)
PREMISE 1 PREMISE 2 CONJOIN PREMISES TEST IMPLICATION
A B | A->B A B | A A B |(A->B)& A A B |(A->B)& A -> B
__________ _________ ______________ ___________________
0) 0 0 | 1 0 0 | 0 0 0 | 0 0 0 | 0 1 0
1) 0 1 | 1 0 1 | 0 0 1 | 0 0 1 | 0 1 1
2) 1 0 | 0 1 0 | 1 1 0 | 0 1 0 | 0 1 0
3) 1 1 | 1 1 1 | 1 1 1 | 1 1 1 | 1 1 1
__________ _________ ______________ ___________________
^
ARGUMENT IS VALID
By Premise 1, A->B, so A is inside B.
By Premise 2, x is inside A.
Therefore, x is inside B.
2. INDIRECT REASONING
If you volunteer to assist, you will benefit with bonus points.
You did not benefit with bonus points.
Therefore, you did not volunteer to assist.
A = You volunteer to assist.
B = You benefit with bonus points.
Premise 1: A -> B (If you assist, then you will benefit.)
Premise 2: -B (You did not benefit.)
Conclusion: -A (You did not assist.)
PREMISE 1 PREMISE 2 CONJOIN PREMISES TEST IMPLICATION
A B | A->B A B | -B A B |(A->B)& -B A B |(A->B)& -B -> -A
__________ _________ ______________ _____________________
0) 0 0 | 1 0 0 | 1 0 0 | 1 0 0 | 1 1 1
1) 0 1 | 1 0 1 | 0 0 1 | 0 0 1 | 0 1 1
2) 1 0 | 0 1 0 | 1 1 0 | 0 1 0 | 0 1 0
3) 1 1 | 1 1 1 | 0 1 1 | 0 1 1 | 0 1 0
__________ _________ ______________ _____________________
^
ARGUMENT IS VALID
By Premise 1, A->B, so A is inside B.
By Premise 2, x is outside B.
Therefore, x is also outside A.
3. DISJUNCTIVE REASONING
Either Mr. Allman shaved himself, or the Barber shaved him.
Mr. Allman did not shave himself.
Therefore, the Barber must have shaved him.
A = Mr. Allman shaved himself.
B = The Barber shaved Mr. Allman.
Premise 1: A + B (Allman shaved himself or the Barber shaved him.)
Premise 2: -A (Not true that Allman shaved himself.)
Conclusion: B (Barber shaved Allman.)
PREMISE 1 PREMISE 2 CONJOIN PREMISES TEST IMPLICATION
A B | A + B A B | -A A B | A+B & -A A B | A+B & -A -> B
___________ _________ ______________ _____________________
0) 0 0 | 0 0 0 | 1 0 0 | 0 0 0 | 0 1 0
1) 0 1 | 1 0 1 | 1 0 1 | 1 0 1 | 1 1 1
2) 1 0 | 1 1 0 | 0 1 0 | 0 1 0 | 0 1 0
3) 1 1 | 1 1 1 | 0 1 1 | 0 1 1 | 0 1 1
___________ _________ ______________ _____________________
^
ARGUMENT IS VALID
By Premise 1, x is in either A or B.
By Premise 2, x is outside A.
Therefore, x must be inside B.
4. CONVERSE REASONING
All terrorists are Arabs.
You are an Arab.
That means you are a terrorist.
A = You are an Arab.
B = You are a terrorist.
Premise 1: B -> A (If you are a terrorist, then you are an Arab.)
Premise 2: A (You are an Arab.)
Conclusion: B (You are a terrorist.)
PREMISE 1 PREMISE 2 CONJOIN PREMISES TEST IMPLICATION
A B | B -> A A B | A A B |(B->A)& A A B |(B->A)& A -> B
___________ _________ ______________ _____________________
0) 0 0 | 1 0 0 | 0 0 0 | 0 0 0 | 0 1 0
1) 0 1 | 0 0 1 | 0 0 1 | 0 0 1 | 0 1 1
2) 1 0 | 1 1 0 | 1 1 0 | 1 1 0 | 1 0 0
3) 1 1 | 1 1 1 | 1 1 1 | 1 1 1 | 1 1 1
___________ _________ ______________ _____________________
^
ARGUMENT IS INVALID
By Premise 1, B is inside A.
By Premise 2, x is inside A.
However, x may or may not be inside B.
Specifically, some Arabs may not be terrorists,
and some terrorists may be Irish.
Timothy McVeigh was neither.
5. INVERSE REASONING
All fanatics are terrorists.
But I am no fanatic.
So, I am no terrorist.
A = I am a fanatic.
B = I am a terrorist.
Premise 1: A -> B (If you are a fanatic, then you are a terrorist.)
Premise 2: -A (I am not a fanatic.)
Conclusion: -B (I am not a terrorist.)
PREMISE 1 PREMISE 2 CONJOIN PREMISES TEST IMPLICATION
A B | A -> B A B | -A A B |(A->B)& -A A B |(A->B)& -A -> -B
___________ _________ ______________ _____________________
0) 0 0 | 1 0 0 | 1 0 0 | 1 0 0 | 1 1 1
1) 0 1 | 1 0 1 | 1 0 1 | 1 0 1 | 1 0 0
2) 1 0 | 0 1 0 | 0 1 0 | 0 1 0 | 0 1 1
3) 1 1 | 1 1 1 | 0 1 1 | 0 1 1 | 0 1 0
___________ _________ ______________ _____________________
^
ARGUMENT IS INVALID
By Premise 1, A is inside B.
By Premise 2, x is outside A.
However, x may or may not be outside B.
Specifically, some terrorists may not be fanatics,
and some non-fanatics may very well indeed be terrorists.
6. CHAIN REASONING
Ottawa is in Ontario.
I am visiting Ottawa.
So, I am also visiting Ontario.
A = I am in Ontario.
B = I am in Ottawa.
Premise 1: B -> A (If I am in Ottawa, then I am in Ontario.)
Premise 2: B (I am in Ottawa.)
Conclusion: A (I am in Ontario.)
PREMISE 1 PREMISE 2 CONJOIN PREMISES TEST IMPLICATION
A B | B -> A A B | B A B |(B->A)& B A B |(B->A)& B -> A
___________ _________ ______________ _____________________
0) 0 0 | 1 0 0 | 0 0 0 | 0 0 0 | 0 1 0
1) 0 1 | 0 0 1 | 1 0 1 | 0 0 1 | 0 1 0
2) 1 0 | 1 1 0 | 0 1 0 | 0 1 0 | 0 1 1
3) 1 1 | 1 1 1 | 1 1 1 | 1 1 1 | 1 1 1
___________ _________ ______________ _____________________
^
ARGUMENT IS VALID
By Premise 1, B is inside A.
By Premise 2, some x is inside B.
Therefore, x must be inside A also.
Notice the similarity to the direct reasoning diagram.
NOTE that the () are necessary in (A -> B) & A -> B to distinguish premises.
Otherwise, the order of operations would interpret A -> B & A -> B as A -> (B & A) -> B,
which is not the same as (A -> B) & A -> B .
So be careful, or you will get the wrong results.
ASSIGNMENT:
After you understand the varieties of valid arguments,
prove or disprove one of the arguments below.
In other words, show that the argument is valid or invalid.
Post your argument, before anyone else,
with its diagram and truth tables in a comment
and receive 7 points = 4 points for table + 3 points for diagram.
- Copy and paste your argument into a comment.
- Determine the simple sentences A and B.
- Convert Premise 1 to symbols.
- Convert Premise 2 to symbols.
- Convert Conclusion to symbols.
- Receive 4 points for the truth table if it contains all five correct columns:
- Premise 1
- Premise 2
- Conjunction &
- Conclusion
- Implication
- Plus 3 points for the correct diagram,
- containing simple sentences A and B
- with the validity of the argument.
Let A and B represent the simple statements in your argument.
If necessary, be creative when you reduce an argument down to 2 simple statements.
Some of these arguments need rewording before you can analyze them.
Some statements may say the same thing with very different words.
Careful: leave out the negations!
The leading statements are premises. The last statement is the conclusion.
Conjunct the premises together into one compound sentence in a truth table.
Does it imply the conclusion on all rows?
If so, you have proven a valid argument.
Otherwise, the argument is invalid.
You only need to post the last table. The first 3 are for practice.
READ THIS SLOWLY:
If someone finishes a problem that you began but did not finish correctly,
they get the points, and you must select another argument.
HINTS:
Drag the circles around in the applet to where you think they should go.
You only need 6 configurations for the problems below.
Your problem is one of these 6.
You may need to switch the A and B circles.
Press the left and right arrows to switch the A and B circles.
Let A and B represent the simple statements in your argument.
If necessary, be creative when you reduce an argument down to 2 simple statements.
Some of these arguments need rewording before you can analyze them.
Some statements may say the same thing with very different words.
Note that if your simple statements A and B are simple, you will earn an extra point.
So do not be impulsive.
Stop and examine your simple statements.
If they contain an OR, AND, BUT, IF, or any conjunction;
or if they contain any negation like NOT and NEVER,
then your statements are not simple.
You get one chance before I tell you what they are.
You can learn more about truth tables by doing a Google Search.
Here is one of the web sites I found on Truth Tables.
Click here for a Validity Demo.
25 ARGUMENTS:
mostly from comments on talk radio
1.
Love is blind.
I did it till I went blind.
It must be love.
2.
Love is blind.
It must be love.
I did it till I went blind.
3.
All men are created equal.
Women are not men.
Therefore, they are not men's equal.
4.
Practice makes perfect.
I haven't practiced in 20 years.
Guess I'll never be perfect.
5.
No man is an island.
Manhattan is an island.
So, Manhattan is not a man.
6.
If the power drill is left on the floor, the baby will get hurt.
The power drill is not on the floor,
so the baby will not get hurt.
7.
All hounds catch rabbits.
You never caught a rabbit.
You ain't nothing like a hound dog.
8.
All U.S. Presidents must be born in the United States.
Scwarzenegger was born in Austria.
Scwarzenegger will never be president.
9.
Every Friday the 13th, something bad happens.
Thank goodness, it's not Friday the 13th.
Nothing bad is going to happen.
10.
Plato believed Socrates was immortal, and more than just a mere man.
But Socrates knew he was only a man, and
therefore, he had to die some day.
11.
The Constitution of the United States guarantees me the right to bear arms.
The atomic bomb I made in my basement this morning is armed and ready to blow.
Therefore, I have the right to bear it.
12.
Every year we create more and more gas guzzlers,
and every year the Earth gets hotter.
We must limit our gas guzzling, or we will all fry in our own fat.
13.
They say that smoking kills you.
But, hey, I've smoked a pack a day all my life,
and I ain't dead yet.
14.
If cigarettes were lethal, I would have been dead a long time ago.
As you can see, I ain't dead yet.
So cigarettes can't be all that lethal.
15.
They will find WMDs, or they will go to war.
They did not find any WMDs.
So they will go to war.
16.
They have caught us off guard many times,
and everyday they grow stronger.
So this time, we must get them before they get us,
or they will grow even stronger.
17.
What you do for others when they are in need,
will be done for you when you are in need.
So, if you need help in hard times, give help in good times.
18.
We cannot believe in something that we cannot conceive of.
However, the one and only true God is totally inconceivable.
This means that the God we believe in is not the true God.
19.
Either Hillary will run, or John McCain will run, but not both.
John McCain drops out.
So, Hillary decides not to run.
20.
An armed world is a polite world.
Every nation will soon have its own atomic bomb.
So all nations will be very polite to each other.
21.
Yeshooah died for my sins.
But gods cannot die.
Therefore, Yeshooah is not a god.
22.
The Barber of Trimville must shave himself,
yet the Barber is not allowed to shave himself.
Therefore, everything is beautiful in its own way.
23.
The answer is true.
The answer is false.
If the answer is both true and false, then to be or not to be is the question.
24.
To be is the question.
Not to be is the question.
If to be or not to be is the question, then the answer is both true and false.
25.
If the conclusion of a valid argument is true, then its premises are true.
Assume, however, that the premises of a valid argument are false.
Then its conclusion is also false.
26.
All snarks are boojums.
It was not a snark.
Then it was not a boojum or a snark.
27.
No blog is a wiki.
This is a blog.
Therefore, this is not a wiki.
26. All blogs are wikis. This is a blog. Therefore this is a wiki.
27. All blogs are wikis. This is a wiki. Therefore this is a blog.
28. All blogs are wikis. This is not a blog. Therefore this is a wiki.
29. All blogs are wikis. This is not a blog. Therefore this is not a wiki.
30. All blogs are wikis. This is not a wiki. Therefore this is a blog.
31. All blogs are wikis. This is not a wiki. Therefore this is not a blog.
32. All wikis are blogs. This is a blog. Therefore this is a wiki.
33. All wikis are blogs. This is a not a blog. Therefore this is a wiki.
34. All wikis are blogs. This is a not a blog. Therefore this is not a wiki.
35. All wikis are blogs. This is a not a wiki. Therefore this is a blog.
36. All wikis are blogs. This is a not a wiki. Therefore this is not a blog.
37. All wikis are blogs. This is a wiki. Therefore this is a blog.
38. If it's a snark, then it's a boojum. It was no boojum. Then it must have been a snark.
39. If it's a snark, then it's a boojum. It was no boojum. Then it must not have been a snark.
40. If it's a snark, then it's a boojum. It was no snark. Then it must have been a boojum.
41. If it's a snark, then it's a boojum. It was no snark. Then it must not have been a boojum.
42. No blog is a wiki. This is a blog. Therefore this is not a wiki.
43. No blog is a wiki. This is a wiki. Therefore this is not a blog.
44. No wiki is a blog. This is a blog. Therefore this is not a wiki.
45. No wiki is a blog. This is a wiki. Therefore this is not a blog.
46. This is either a blog or a wiki. This is not a blog. Therefore this is a wiki.
47. This is either a blog or a wiki. This is not a blog. Therefore this is not a wiki.
48. This is either a blog or a wiki. This is not a wiki. Therefore this is a blog.
49. This is either a blog or a wiki. This is not a wiki. Therefore this is not a blog.
50. This is neither a blog nor a wiki. This is not a blog. Therefore this is a wiki.
51. This is neither a blog nor a wiki. This is not a blog. Therefore this is not a wiki.
52. This is neither a blog nor a wiki. This is not a wiki. Therefore this is a blog.
53. This is neither a blog nor a wiki. This is not a wiki. Therefore this is not a blog.
Comments:
From wHolt - 2/14/06 10:10 PM
From wHolt - 2/14/06 10:51 PM
HINT:
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 | (Premise 1 | & | Premise 2) | -> | Conclusion | |
| 0 | 0 | ||||||
| 0 | 1 | ||||||
| 1 | 0 | ||||||
| 1 | 1 |
Comments:
From wHolt - 12/14/06 10:20 PM
GolfGirl - your premise 2 says I am not dead
Which is it?
You are confusing simple statements A and B
with your premise statements.
no-no...
From GolfGirl - 12/14/06 4:00 PM
#14. If cigarettes were lethal, I would have been dead a long time ago. As you can see, I am not dead yet. So cigarettes can't be all that lethal.
Indirect Reasoning
A=If cigarettes were lethal, I would have been dead long ago.
B= I am dead
Premise 1: A->B (Cigarettes are lethal.)
Premise 2: -B (I am dead )
Conclusion- -A (Cigarettes are lethal.)
PREMISE 1 PREMISE 2 CONJOIN PREMISES TEST IMPLICATION
A B | A -> B A B | -B A B | -A->B & -A A B | A->B & -A -> -B
___________ _________ ______________ _____________________
0) 0 0 | 1 0 0 | 0 0 0 | 1 0 0 | 0 1 1
1) 0 1 | 1 0 0 | 1 0 1 | 1 0 1 | 1 1 0
2) 1 0 | 0 1 0 | 0 1 0 | 0 1 0 | 0 1 1
3) 1 1 | 1 0 0 | 0 1 1 | 0 1 1 | 0 1 0
___________ _________ ______________ _____________________
Argument is valid!
From BassLady - 12/13/06 10:51 AM
If I smoke, I will die (A -> B)
I smoke and I ain't dead (A & -B)
Conclusion (A ->B) & (A & -B)
Would this be an accurate conclusion???? Then I will post the table--AGAIN!!
From wHolt - 12/12/06 11:57 AM
BassLady
+ means OR.
There is no OR in the argument,
so dont put one in .
From BassLady - 12/11/06 9:43 AM
Okay before I post everything again................
Premise 1 - If you smoke you will die (A ->B)
Conclusion - I smoke and I ain't dead (A & -B)
(A ->B) + (A & -B)
Am I closer with this?
From wHolt - 12/10/06 9:50 AM
Bubba - I cannot improve upon the instructions without your input.
Maybe you can tell me what you are confused about?
Basslady-
A=I smoke
B=I die
Conclusion = I smoke & I ain't dead
notice that the conclusion has an AND in it. Not an IF.
also notice that your diagram says "If I die, then I smoke."
From BassLady - 12/9/06 10:02 PM
From BassLady - 10/29/06 11:45 AM
#13 - They say that smoking kills you, but hey I have smoked a pack a day all my life and I ain't dead yet.
Not Valid
1 - If I smoke - I will die
conclusion - I smoke and I ain't dead
| A | B | (A->B) | & | A | -> -B |
| 0 | 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 | 0 |
From Bubba - 12/9/06 7:34 AM
From wHolt - 12/7/06 11:01 AM
DirtyBird- dont make up the premise when it is clearly something else.
From DirtyBird - 12/6/06 6:56 PM
From wHolt - 12/6/06 12:05 PM
DirtyBird-
Premise 1 = This is neither a blog nor a wiki.
There is no implication in this.
So dont use the arrow ->
See if you can symbolize premise 1.
Bubba-
do not confuse premises with simple statements.
premise 1 is not a simple statement
altho premise 2 and the conclusion are.
however, you switched A and B in mid argument.
fix it.
From Bubba - 12/6/06 10:26 AM
2.
Love is blind.
It must be love.
I did it till I went blind.
Premis 1: i am in love
Premis 2: i am blind
Conclusion: i did it till i went blind.
Premis 1: A -> B
Premis 2: B
Consclusion: A&B -> A
P1
| A | B | A->B |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
P2
| A | B | B |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Conclusion
| A | B | A & B -> A |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
TEST IMPLICATION
| A | B | (A->B | & | B) | -> | A&B | |
| 0 | 0 | 0 | 0 | 0 | |||
| 0 | 1 | 0 | 1 | 0 | |||
| 1 | 0 | 0 | 0 | 0 | |||
| 1 | 1 | 1 | 1 | 1 |
From DirtyBird - 12/5/06 6:35 PM
This is neither a blog nor a wiki.
This is not a wiki.
Therefore, this is not a blog.
27) Premise1= If this is a blg, then it is not a wiki.
Premise2= This is a blog.
Conclusion= This is nt a wiki.
A= This is a blog.
B= This is a wiki.
Premise 1:
| A | B | A->-B | |
| 0 | 0 | 1 | |
| 0 | 1 | 1 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Premise 2:
| A | B | A | |
| 0 | 0 | 0 | |
| 0 | 1 | 0 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Conjoin Premises:
| A | B | (A->B) & A | |
| 0 | 0 | 1 | |
| 0 | 1 | 0 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Test Implication:
| A | B | (A->-B) | & | A) | -> | -B | |
| 0 | 0 | 1 | 1 | 0 | 1 | 1 | |
| 0 | 1 | 1 | 0 | 0 | 1 | 0 | |
| 1 | 0 | 1 | 1 | 1 | 1 | 1 | |
| 1 | 1 | 0 | 0 | 0 | 1 | 0 |
From wHolt - 11/23/06 10:22 AM
#13 -
Premise 1 - They say that smoking kills you.
Conclusion -but hey I've smoked a pack a day all my life and I ain't dead yet.
Premise 1 - If I smoke I will die = (A->B) OK
Conclusion - I smoke AND I ain't dead. fix!
Premise 1 => Conclusion
(Congrats on the NOT smoking!)
From BassLady - 11/22/06 9:42 PM
You still have me to torture you! I just cannot get this, but I do not want to give up. This is try #275 
| A | B | (A ->B) | & | -B |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 | 0 |
#13 - They say that smoking kills you, but hey I've smoked a pack a day all my life and I ain't dead yet.
Premise 1 - If I smoke I will die
Conclusion - I smoke and I ain't dead.
(The good news is that I hate this puzzle so much that I quit smoking. 3 weeks today!!!)
From wHolt - 11/20/06 9:49 AM
From Draco - 11/19/06 11:13 PM
27.
Premise 1=If this is a blog, then it is not a wiki.
Premise 2=This is a blog.
Conclusion=This is not a wiki.
A=This is a blog.
B=This is a wiki.
Premise 1:
| A | B | A->-B | |
| 0 | 0 | 1 | |
| 0 | 1 | 1 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Premise 2:
| A | B | A | |
| 0 | 0 | 0 | |
| 0 | 1 | 0 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Conjoin Premises:
| A | B | (A->-B) & A | |
| 0 | 0 | 1 | |
| 0 | 1 | 0 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Test Implication:
| A | B | ((A->-B) | & | A) | -> | -B | |
| 0 | 0 | 1 | 1 | 0 | 1 | 1 | |
| 0 | 1 | 1 | 0 | 0 | 1 | 0 | |
| 1 | 0 | 1 | 1 | 1 | 1 | 1 | |
| 1 | 1 | 0 | 0 | 0 | 1 | 0 |
ARGUMENT IS VALID
* NINTH CORRECTION*
From wHolt - 11/15/06 11:54 AM
Draco - now for your diagram...
It says "If it's a wiki, then it's a blog". (B=>A)
But that is not what your statement or your notation say (A=>~B)
From Draco - 11/14/06 8:22 PM
27.
Premise 1=If this is a blog, then it is not a wiki.
Premise 2=This is a blog.
Conclusion=This is not a wiki.
A=This is a blog.
B=This is a wiki.
Premise 1:
| A | B | A->-B | |
| 0 | 0 | 1 | |
| 0 | 1 | 1 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Premise 2:
| A | B | A | |
| 0 | 0 | 0 | |
| 0 | 1 | 0 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Conjoin Premises:
| A | B | (A->-B) & A | |
| 0 | 0 | 1 | |
| 0 | 1 | 0 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Test Implication:
| A | B | ((A->-B) | & | A) | -> | -B | |
| 0 | 0 | 1 | 1 | 0 | 1 | 1 | |
| 0 | 1 | 1 | 0 | 0 | 1 | 0 | |
| 1 | 0 | 1 | 1 | 1 | 1 | 1 | |
| 1 | 1 | 0 | 0 | 0 | 1 | 0 |
ARGUMENT IS VALID
* EIGHTH CORRECTION*
From wHolt - 11/11/06 12:05 AM
#13 - They say that smoking kills you,
but hey I smoked a pack a day all my life and I ain't dead yet.
Premise 1 - If I smoke, then I die [ <=change premise 1]
Conclusion - I smoke and I ain't dead yet.
now notate these statements accordingly:
premise 1 is an if-then
conclusion contains an AND and a NOT
From BassLady - 11/10/06 9:21 PM
| A | B | A | A ->B | |
| 0 | 0 | 0 | 1 | |
| 0 | 1 | 1 | 1 | |
| 1 | 0 | 0 | 0 | |
| 1 | 1 | 0 | 1 |
#13 - They say that smoking kills you, but hey I smoked a pack a day all my life and I ain't dead yet.
Premise 1 - I smoke and I die
Conclusion - I smoke and I ain't dead yet.
From wHolt - 11/8/06 10:04 AM
Draco -
this one:
| A->(-B | & | A) | -> | -B |
equals this one
| (A->-B | & | A) | -> | -B |
because of the order of operations.
(& before =>)
what you want is :
| (A->-B) | & | A | -> | -B |
which is the same as :
| ((A->-B) | & | A) | -> | -B |
Also correct your diagram to express your argument.
From Draco - 11/7/06 8:58 PM
27.
Premise 1=If this is a blog, then it is not a wiki.
Premise 2=This is a blog.
Conclusion=This is not a wiki.
A=This is a blog.
B=This is a wiki.
Premise 1:
| A | B | A->-B | |
| 0 | 0 | 1 | |
| 0 | 1 | 1 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Premise 2:
| A | B | A | |
| 0 | 0 | 0 | |
| 0 | 1 | 0 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Conjoin Premises:
| A | B | (A->-B) & A | |
| 0 | 0 | 1 | |
| 0 | 1 | 0 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Test Implication:
| A | B | (A->-B | & | A) | -> | -B | |
| 0 | 0 | 1 | 1 | 0 | 1 | 1 | |
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | |
| 1 | 0 | 1 | 1 | 1 | 1 | 1 | |
| 1 | 1 | 0 | 0 | 0 | 1 | 0 |
ARGUMENT IS INVALID
* SEVENTH CORRECTION*
From wHolt - 11/7/06 11:20 AM
| A->(-B | & | A) | -> | -B |
Draco - () are in wrong place.
Try this:
| (A->-B | & | A) | -> | -B |
or this:
| (A->-B) | & | A | -> | -B |
It may or may not make a difference.
Test it.
Notice also that your diagram says all B's are A's. But your premise 1 disagrees.
From Draco - 11/6/06 3:21 PM
27.
Premise 1=If this is a blog, then it is not a wiki.
Premise 2=This is a blog.
Conclusion=This is not a wiki.
A=This is a blog.
B=This is a wiki.
Premise 1:
| A | B | A->-B | |
| 0 | 0 | 1 | |
| 0 | 1 | 1 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Premise 2:
| A | B | A | |
| 0 | 0 | 0 | |
| 0 | 1 | 0 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Conjoin Premises:
| A | B | (A->-B) & A | |
| 0 | 0 | 1 | |
| 0 | 1 | 0 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Test Implication:
| A | B | A->(-B | & | A) | -> | -B | |
| 0 | 0 | 1 | 1 | 0 | 1 | 1 | |
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | |
| 1 | 0 | 1 | 1 | 1 | 1 | 1 | |
| 1 | 1 | 0 | 0 | 0 | 1 | 0 |
ARGUMENT IS INVALID
* SIXTH CORRECTION*
From wHolt - 11/4/06 2:20 PM
Premise 1: They say that smoking kills you,
Conclusion: Hey I have smoked a pack a day all my life and I ain't dead yet.
Premise1 => Conclusion ?
You only need to convert these statements to symbols and test.
There is no premise 2.
From BassLady - 11/3/06 8:23 PM
From wHolt - 10/30/06 11:32 AM
BassLady - does
If I smoke then I will die
imply
I smoke and I ain't dead
?
convert to symbols and test for validity.
almost...
From BassLady - 10/29/06 11:45 AM
| A | B | A -> B | |
| 0 | 0 | 1 | |
| 0 | 1 | 1 | |
| 1 | 0 | 0 | |
| 1 | 1 | 1 | |
|
#13 - They say that smoking kills you, but hey I have smoked a pack a day all my life and I ain't dead yet.
Not Valid
1 - If I smoke - I will die
conclusion - I smoke and I ain't dead
From wHolt - 10/25/06 12:00 PM
Draco - this is the problem:
without (),
A => ~B & A => ~B is equal to A => (~B & A) => ~B
But your argument is this:
(A => ~B) & A => ~B
The order of operations puts & before =>
Add the () and resubmit. Thanks.
From Draco - 10/24/06 7:57 PM
27.
Premise 1=If this is a blog, then it is not a wiki.
Premise 2=This is a blog.
Conclusion=This is not a wiki.
A=This is a blog.
B=This is a wiki.
Premise 1:
| A | B | A->-B | |
| 0 | 0 | 1 | |
| 0 | 1 | 1 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Premise 2:
| A | B | A | |
| 0 | 0 | 0 | |
| 0 | 1 | 0 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Conjoin Premises:
| A | B | (A->-B) & A | |
| 0 | 0 | 1 | |
| 0 | 1 | 0 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
Test Implication:
| A | B | (A->-B) | & | A | -> | -B | |
| 0 | 0 | 1 | 1 | 0 | 1 | 1 | |
| 0 | 1 | 1 | 0 | 0 | 1 | 0 | |
| 1 | 0 | 1 | 1 | 1 | 1 | 1 | |
| 1 | 1 | 0 | 0 | 0 | 1 | 0 |
ARGUMENT IS VALID
* FIFTH CORRECTION*
From wHolt - 10/24/06 11:07 AM
7Iron- notice that I am suggesting different simple statements:
A = Yeshooah is a god
B = Yeshooah died
From 7Iron - 10/23/06 1:47 PM
Mr. Holt,
I read your comment but my last posting is what I got out of it. It appears, I will be
Premise 1: All volunteers to assist will benefit with bonus points.
Premise 2: You did not benefit with bonus points.
Conclusion: Therefore, you did not volunteer to assist.
Simple Statements:
A = You volunteer to assist.
B = You benefit with bonus points.
Premise 1: A -> B (If you assist, then you will benefit.)
Premise 2: -B (You did not benefit.)
Conclusion: -A (You did not assist.)
PREMISE 1
PREMISE 2
CONJOIN PREMISES
TEST IMPLICATION
Argument is VALID