Wiki Menu

Home
Pix
Get Hoversnap
Use Hoversnap
Survey
Puzzles
Doodles
3 Ladies
3 Prisoners
CSG
AlphaSets
Subsets
Match Sets
Pizza Test
Truth Tables
Conditionals
16 Tables
Validity
Arguments
Pipe Game
Water Logic
Adder
Carry In
Carry Out
8-Car Adder
Number Bases
ASCII
Codes
RSA
Sequences
Staircase
Counting
ScrabbleGrams
Anagrams
Dupligrams
Amalgams
Powerball
Birthdays
Dice Rolls
BlackJack
Coin Flip
Triangle Tree

Subsets



The applet above allows you to shade and type. By clicking the mouse inside the applet, you can shade any of the 4 regions the circles create. As in the previous exercise, place the letters from your celebrity's A and B sets into their appropriate regions. Point the mouse where you want a letter, and type it. Letters belonging to both A and B go in the middle. Letters not in either A or B go outside the circles. To delete a letter, point at it, and hit the Escape or Delete key.

In this exercise, you will translate words into set operators.
Here is a table of common synonyms for set operators:

Click here for a Subsets Demo.

SYNONYMS FOR SET OPERATORS

 +        &           —           —
OR      AND         NOT         LESS

add     intersect   complement  subtract
union   both        inverse     difference
either  overlap     negation    extraction
merge   common      opposite    without




Beginners often confuse + with AND. This is the most common error in set translations. Don't do it. A AND B means what is in BOTH A AND B. A OR B means what is in EITHER A OR B.

In English, OR means Either A or B, or both A and B. I am thinking about buying either a Chevy or a Ford today. This is an example of an Inclusive OR. If we want to exclude both A and B in an OR statement, we would say Either A or B, but not both. This is an example of the Exclusive OR: I will drive either my Chevy or my Ford to work today.

Notice that NOT and LESS both use the – symbol.
There is an analogy in arithmetic.
We use – for negative numbers and also for subtraction.
For example: –3 = 0–3
(negative 3 is zero minus 3)
Similarly with sets: –A = U–A
(what is NOT in set A is our Universal set LESS what is in set A)


ASSIGNMENT

 Below are exercises using the Alphabet as our universal set. Although each of you have different A and B sets, all of you are using the alphabet as your universal set. Each exercise refers to subsets of the alphabet. A SUBSET is a set that is part of a bigger set. If X is a subset of Y, then every element in X is an element in Y. Your A and B sets are each subsets of the alphabet. What is not in your A or B sets is also a subset of the alphabet.

Your job is to translate the words, NOT AND OR, into set notation, and then find the corresponding subset (regions) on your diagram. Parentheses are important, as in algebra. NOT (A OR B) is not the same as NOT A OR B. The NOT has precedence over an AND. And the AND has precedence over an OR.
  1. ((A OR B) AND (NOT A)) OR ((A OR B) AND (NOT B))
  2. ((A OR B) AND (NOT B)) AND B
  3. ((NOT A) AND (NOT B)) OR ((NOT B) AND (NOT B))
  4. ((NOT A) AND (NOT B)) OR (NOT B)
  5. ((NOT A) AND (NOT B)) OR NOT B
  6. ((NOT A) AND B) OR (NOT (A OR B))
  7. ((NOT A) OR (NOT B)) AND ((NOT B) OR (NOT B))
  8. ((NOT A) OR (NOT B)) AND (NOT B)
  9. ((NOT A) OR (NOT B)) AND (NOT B))
  10. ((NOT A) OR B) AND B
  11. ((NOT A) OR NOT B) AND ((NOT B) OR (NOT B))
  12. ((NOT A)) OR (NOT B)
  13. ((NOT B) AND (NOT B)) AND (B AND (NOT A))
  14. ((NOT B) AND (NOT B)) AND (B AND B)
  15. ((NOT B) AND (NOT B)) AND (NOT B)
  16. ((NOT B) AND (NOT B)) OR ((NOT A) AND (NOT B))
  17. ((NOT B) AND (NOT B)) OR ((NOT B) OR B)
  18. ((NOT B) AND B) AND A
  19. ((NOT B) AND B) AND B
  20. (A AND (NOT B)) AND (B AND (NOT A))
  21. (A AND (NOT B)) OR (B AND (NOT A))
  22. (A AND (NOT B)) OR (B AND (NOT B))
  23. (A AND B ) OR (NOT (A OR B))
  24. (A AND B) OR (A AND B)
  25. (A AND B) OR (NOT A) OR B
  26. (A AND B) OR (NOT B)
  27. (A AND B) OR B
  28. (A OR (NOT B)) AND (B OR (NOT A))
  29. (A OR B) AND ((NOT A) OR (NOT B))
  30. (A OR B) AND (A OR B)
  31. (A OR B) AND (NOT ((NOT A) AND B))
  32. (A OR B) AND (NOT (A AND B))
  33. (A OR B) AND (NOT (B OR B))
  34. (A OR B) AND (NOT B)
  35. (A OR B) AND B
  36. (B AND (NOT B)) AND ((NOT B) AND (NOT A))
  37. (B AND (NOT B)) AND (B AND A)
  38. (B AND (NOT B)) OR A
  39. (B AND (NOT B))) AND B
  40. (B AND B) AND (B OR B)
  41. (B OR (NOT B)) AND (B AND B)
  42. (B OR (NOT B)) OR (NOT B)
  43. (B OR B) AND (B OR B)
  44. (B OR B) AND (NOT A)
  45. (NOT (A AND B)) AND (NOT (B AND B))
  46. (NOT A) AND (NOT B)
  47. (NOT A) AND (NOT B) AND (NOT B)
  48. (NOT A) OR (NOT B)
  49. (NOT A) OR (NOT B) OR (NOT B)
  50. (NOT A) OR B
  51. (NOT B) AND ((NOT B) OR B)
  52. (NOT B) AND (B AND A)
  53. (NOT B) AND (B OR A)
  54. (NOT B) AND B
  55. (NOT B) OR ((NOT B) AND (NOT B))
  56. (NOT B) OR (NOT B)
  57. A AND ((NOT B) OR (NOT B))
  58. A AND (A OR B)
  59. A AND (B AND (NOT B))
  60. A OR ((NOT B) AND (NOT B))
  61. A OR (A AND B)
  62. A OR (B AND (NOT B))
  63. A OR (B AND B)
  64. B AND ((NOT A) AND (NOT B))
  65. B AND (B AND B)
  66. B AND (NOT ((NOT A) AND B))
  67. B AND B
  68. B OR (NOT B)
  69. B OR B
  70. NOT ((A AND B) OR (B AND B))
  71. NOT (A AND B AND B)
  72. NOT (A AND B)
  73. NOT (A OR B OR B)
  74. NOT (A OR B)
  75. NOT (B AND B)
  76. NOT (NOT A)
Translate only ONE of these exercises into set notation using the symbols + & - . Using the applet at the top of the page, shade those regions that your notation refers to. Then type, into the areas you shaded, and only those areas, the letters in your celebrity sets A and B that your notation refers to. Place your completed exercise in a comment. Along with your celebrity's name and birthplace, tell us the number of the exercise you are doing, copy the expression, and enter its equivalent notation.

Oh, one other thing, if someone has already completed your exercise, you must do another that no one has yet placed in a comment. So you may want to check the comments first before you begin.

This exercise is worth 3 points: 1 for notation, 1 for the letters, and 1 for shading in the proper region(s). Help your neighbor if they need correcting. That way everyone gets points. If someone corrects you, and they are wrong, recorrect them nicely.



Here are some examples to get you started using our celebrity data: 

George W. Bush
New Haven, Connecticut


A = {GEORWBUSH}
B = {NEWHAVCOTIU}
1. A OR B = A + B = {GBRSWHOEUNVCIAT}

AB Venn


2. A AND B = A & B = {WHOEU}

AB Venn


3. A LESS B = A – B = {GBRS}

AB Venn


4. NOT A = –A = {NVCIATFKMPQXZDYJL}

AB Venn


5. A AND NOT B = A & –B = {GBRS}

AB Venn


6. B AND NOT B = B & –B = { } = Ø

AB Venn

Note that when a set does not exist, we indicate it with a slashed zero Ø.
To type a Ø, hold down the alt key and, on the number pad, enter 0216



WHICH SETS ARE EQUAL?
Start thinking about which of these exercises express the same subsets. That will be your next assignment.

EXAMPLE:
Set 3 = Set 5
To subtract a set B from another set A is the same as intersecting set A with the complement of set B.

Comments:

From wHolt - 12/10/06 9:43 AM

Bubba - not yet. you shaded A-B.
First shade A&B.
Then subtract the parts that are in B.
And only letter the parts that are shaded.

From Bubba - 12/9/06 7:29 AM

From wHolt - 12/7/06 10:59 AM

Bubba - you shaded (A+B)-B

From Bubba - 12/6/06 10:12 AM

(a&b)-b

From wHolt - 12/3/06 1:02 PM

Pac - Put this expression in the set matcher : (-A)+(-B)+(-B)
What do you get?

From Pac - 12/2/06 3:34 PM

Sandra Bullock; Arlington, Virginia

A = {SANDRBULOCK}

B = {ARLINGTOV}

#49: (NOT A) OR (NOT B) OR (NOT B) = (-A)+(-B)+(-B) = {BCDEFHJKMPQSUWXYZ}

From Lexiowen - 11/30/06 10:37 PM

subsets

30. (AOR B) AND (A OR B) = (A + B) & (A + B)

A: EMILY WASTON

B: ISLINGTON LONDON

From Capricorn - 10/2/06 6:09 PM

subset

#7 ((NOT A) OR (NOT B)) AND ((NOT B) OR (NOT B))

= ((-A) + (-B)) & ((-B) + (-B))

HAYAO MIZAKO, TOKYO JAPAN

From Draco - 10/1/06 6:05 PM

 

*Correction*

13.((NOT B) AND (NOT B)) AND (B AND (NOT A)) = (-B & -B) & (B & -A)

Samuel Beckett  Dublin, Ireland

A={SAMUELBCKT}  B={DUBLINREA}

From Poovey - 10/1/06 3:01 PM

I don't know why it took me so long! Whew..................

From wHolt - 10/1/06 2:22 PM

Poovey - What kept you from thinking of this before?

From Poovey - 10/1/06 12:07 PM

(A+B)-B

From wHolt - 9/30/06 1:23 PM

Poovey- add A plus B, then subtract B from it.

From Poovey - 9/29/06 6:12 PM

 

(A OR B) AND NOT B= (A + B) & (-B)

TRYING AGAIN...........SOMEONE PLEASE HELP ME TO GET THIS CLICKED IN MY HEAD IF THIS IS NOT RIGHT

 

From wHolt - 9/29/06 12:22 PM

The & means intersection overlap. The & does not mean +.

From Capricorn - 9/27/06 9:54 PM

I hope this attempt is correct... if not, somebody, please help...I'm lost!

From Poovey - 9/27/06 6:21 PM

#34 (A OR B) AND (NOT B)= (A+B) & (-B)

I THINK THIS IS CORRECTED...................

I DELETED MY OLD ONE

From wHolt - 9/27/06 1:00 PM

THIS PAGE IS NOW CLOSED TO NEWCOMERS!



IF YOU HAVE STARTED YOUR SUBSETS,
BUT DID NOT FINISH, 
CONTINUE TILL YOU GET IT!

Use the Set Matcher applet to check yours!

From Spartan - 9/27/06 11:30 AM

#69  B or B     A= Johnny Depp   B= Owensboro, Kentucky

       B + B     {WSBRKTUC} + {WSBRKTUC}

From Brick - 9/27/06 2:43 AM

#5 ((NOT A) AND (NOT B)) OR NOT B = A & -B = {CBO}

Charles Bronson; Ehrenfield, Pennsylvania

A=CHARLESBON

B=EHRNFILDPSYVA

 

From wHolt - 9/27/06 12:50 AM

ALL OF YOU ON THE LIST BELOW RECEIVE FULL CREDIT!
IF NOT ON THE LIST, STUDY THE EXAMPLES OF THOSE ON THE LIST.
REDO IF NOT ON THE LIST.

7Iron
Aeneid
BassLady
Bob
Boki
Bravo
CatsEyes
Centerfield
Cheana
David
Deuce
DirtyBird
Draco
Fro
Harkar
Hotrod
Houdini
JooJoo
Kathi
Melewen
Pod
Poovey
Pringle
RockClimber
SkoolGirl
Slick
Soller
Sunshine
SuperDuke
Taurus
Troll
Zonino

From Pac - 9/26/06 11:16 PM

Sandra Bullock; Arlington, Virginia

A = {SANDRBULOCK}

B = {ARLINGTOV}

#49: (NOT A) OR (NOT B) OR (NOT B) = (-A)+(-B)+(-B) = {EFHJKMPQWXYZ}

Subsets

From SunSport - 9/26/06 10:05 PM

  DREW CAREY
  CLEVELAND,OHIO
 A (DREWCAY)
 B (CLEVANDOHI)
 #2  ((A OR B) AND (NOT B)) AND B
  ((A + B) & (-B)) & B
  A & B = (DCEA)
  
  
  

From RockClimber - 9/26/06 9:34 PM

Henry "Hank" Louis Aaron, Mobile, Alabama

A={HKSILAEONRUY}     B={MBOEAIL}

#30- (B And Not B) or A= (B&-B)+A= {HKSILAEONRUY}

From Bubba - 9/26/06 9:31 PM

subsets

 

(a&b)-b  number 26

From Pringle - 9/26/06 8:23 PM

 # 42 (B+(-B)) + (-B) = {A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}

  MATTHEW LILLARD   LANSING, MICHIGAN

 A = { MATHEWLIRD}

 B= {LANSIGMCH}

From DirtyBird - 9/26/06 5:35 PM

#63 A or (B&B)

A+(B&B)= {JCNHIAEROUPSTLV}

Johnny Cochran, Shreveport, Louisiana

Let Me Know WHat May Be Wrong WIth This One Or I Am Moving On.

From Pod - 9/26/06 9:51 AM

I think I have it now...

18. ((NOT B) AND B) AND A = ((-B) &B) &A

From SkoolGirl - 9/25/06 8:18 PM

Subsets 1

#26 (A AND B) OR (NOT B)

(A&B)+(-B)

A{BILCNTO} B{HOPEARKNS}

From Phoenix - 9/25/06 7:34 PM

subsets

Mariah Carey

A={MARIHCEY}   B={HUNTIGOEWYRK}

 #56 (NOT B) OR (NOT B) = (-B) + (-B) = +B 

B={HUNTIGOEWYRK} 

 

From Deuce - 9/25/06 6:52 PM

A OR (A AND B)

A={WAYNEGRTZK}

B={BRANTFODI}

From CenterField - 9/25/06 5:18 PM

Subsets

From GolfGirl - 9/25/06 4:37 PM

 #1-  A or B= A+B {TPHBMQUOGY}

Stephen Baldwin

Massapequa, Long Island, New York

From Boki - 9/24/06 8:25 PM

35. (A or B) and B= (A+B)& B=B

From Shanja - 9/24/06 6:43 PM

From Bravo - 9/24/06 3:57 PM

 # 75   Not (B&B) 

Paula Jones, Lonoke ,Arkansas

From David - 9/23/06 11:10 PM

A={CHAKN}  B={CHIAGOLNS}

46. (NOT A) AND (NOT B) = (-A) & (-B) = {BDEFJLPQRTUVWXYZ}

CHAKA KAHN, CHICAGO, ILLINOIS

 

From Harkar - 9/23/06 6:07 PM

#53.  (NOT B) AND (B OR A)       (-B) & (B+A)    Russell Crowe (4/7/1964)

Harkar Subsets.gif

From Fro - 9/21/06 8:32 PM

Problem #44
(B OR B) AND (NOT A) = {CYPA}

A=TIGERWODS
B=CYPRESA

 

From CatsEyes - 9/21/06 7:46 PM

Problem# 74.

NOT (A OR B) = -(A + B) = {BJPQVWXDYZ}

From 7Iron - 9/21/06 11:46 AM

7IRON

#57  Roy Acuff – Maynardsville, Tennessee
 A AND ((NOT B) OR (NOT B)) = {cfou}
 A&((-B)+(-B)) = A&-B


 

From wHolt - 9/20/06 9:02 PM

Use the match sets applet to test your notation!

From Pod - 9/20/06 8:54 PM

Mine's corrected.

From Taurus - 9/20/06 12:30 AM

subset # 27

Johnny Unitas= A{JOHNYUITAS}

Pittsburgh, Pennsylvania= B {PITSBURGHENYLVA}

#27  (A and B)+ B= (A & B) + B {PITSBURGHENYLVA}

From Soller - 9/19/06 9:31 PM

 

 #30. (A or B) AND (A or B)

          (A + B) & ( A +B)

Hugh Jackman......Syndney, Australia

 

From BassLady - 9/19/06 9:10 PM

Subset

Quentin Tarantino - Knoxville, Tennessee

Problem #3     (A and B) or (Not B)  EINOT or AQRUBCDFGHJMPWYZ

(A and B) or (Not B) = A & B - B {EINOTAQRUBCDFGHJMPWYZ}

From Butterfly - 9/19/06 6:09 PM

A. Dana Owens     B. Newark, New Jersey

B OR B = B + B = JKRY

From Cheana - 9/19/06 5:27 PM

#35 (A + B) & B = {ABDEHINOSTU}

From wHolt - 9/19/06 12:07 PM

Those listed below need to reread and redo:

Houdini
Tiger
Spartan
Dirtybird

From Houdini - 9/19/06 9:39 AM

#67 B AND B

B & B = ACDEHILNORSTW

FIXED

From Troll - 9/18/06 7:47 PM

#65 B AND (B AND B), B&(B&B)

A=TOMHANKS B=CONRDALIF

From Tiger - 9/18/06 6:50 PM

William Carlos Williams, Rutherford, New Jersey

#72. Not(A And B)

From Spartan - 9/18/06 6:19 PM

A.  Johnny Depp

B.  Owensboro Kentucky

50.  (NOT A) OR B  =  (-A)+B

From Sunshine - 9/18/06 3:06 PM

A=marycosb

B= lnge

#54 (not b) and b = -B & B = Ø

From wHolt - 9/18/06 11:51 AM

Remember
                           + means OR (union)
                           & means AND (intersection)

Pod and SuperDuke, redo yours.

From Pod - 9/18/06 9:03 AM

Since everyone else has neglected the 'teens...

18. ((NOT B) AND B) AND A = ((-B) &B) &A

A = A D E F I N S T U Y

B = A B C H N U V

From SuperDuke - 9/17/06 10:38 PM

Loretta Lynn

 #20    (A and (not B)) and (B and (not A))

(A & (-B)) & (B & (-A)) = {0}

* Corrected * 09/18/2006

From Bob - 9/17/06 10:03 PM

#67 B AND B = B & B = {burlesontxa}
Kelly Clarkson, Burleson, Texas

 

From JooJoo - 9/17/06 12:31 AM

subset

58. A AND (A OR B)= A & (A +B)= YBUGRAES

GARY BUSEY, GOOSE CREEK TEXAS

From Zonino - 9/17/06 12:07 AM

#24 (A AND B) or (A AND B)

 

From Slick - 9/16/06 10:23 AM

#61  A or (A and B)

Subset

From Aeneid - 9/16/06 10:08 AM

SUBSET PROBLEM 73NOT (A OR B OR B)

From HotrodMinivan - 9/16/06 9:22 AM

Aeneid, I believe if you have Not (A or B or B) that your letters would all be in the middle. You might want to check with WHolt to be sure though.

 

From wHolt - 9/15/06 12:32 PM

Thanks to Melewen , Kathi, and Hotrod.
You only need to letter the areas shaded.
Does anyone wish to help Aeneid?

From Kathi - 9/15/06 7:20 AM

subset

                                     #76

                        NOT(NOT A) = -(-A) = {ZOSGARB}
 

From Melewen - 9/15/06 12:04 AM

Subsets

From HotrodMinivan - 9/14/06 3:44 PM

Subsets #21

From Aeneid - 9/13/06 3:20 PM

NOT (A OR B OR B)

NOT (A OR B OR B)          CORRECTION

From Aeneid - 9/13/06 12:11 AM

NOT (A OR B OR B)

       PROBLEM #73 CELEBRITY SUBSET

       NOT (A OR B OR B)

 

 

 


Last Modified 9/13/06 12:32 AM

Hide Tools

Site
Changes
Index
Search

User
Log In