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– & + ASSIGNMENT ~ Ç È

Check your answers below in the applet above!

#	LEFT	#	RIGHT	ALIAS
	A-B		A & (~B)	wHolt
1	()	17	((~B) & (~C)) & (B & C)	Melewen
51	(~A) & (~B)	83	~(A + B)	kathi
12	((~A)^B)+(~(A^B))	31	(A^(~B))^(B^(~A))	?hotrodminivan
88	Ø	16	((~B)&(~C))&(B&(~A))	Aeneid
68	B	74	B & B	Zonino
26	(A+B)&(~C)	3	((A+B)&(~C))&B	Superduke
32	(A & (~C)) + (B & (~C))	26	(A + B) & (~C)	Pod
38	(B + (~C)) & (B & C)	43	(B&C) & (B+C)	Slick
13	((~A)) + (~B)	48	(~A) + (~B)	Troll
37	(A&B)+B	7	((~A)+B)&B	Butterfly
76	C	77	C+C	Houdini
87	~(~A)	59	A	7Iron
84	~(A & B & C)	49	(~A) + (~B) + (~C)	Sunshine
59	A	65	A & (A+B)	Soller
82	~(A+B+C)	52	(~A) & (~B) & (~C)	Fro
22	(A+B) & ((~A) + (~B))	24	(A+B) & (~(A&B))	Trixie
73	B & (-B)	88	Ø	Bob
2	((A+B) & (~A)) + ((A+B) & (~B))	22	(A+B) & ((~A) + (~B))	Cheana
27	(A + B) & B	74	B & B	HARKAR
59	A	60	A + ((-B)&(-C))	? BRAVO [use the applet]
27.	(A + B) & B	68.	B	Boki
24.	(A+B)&(~(A&B))	2.	((A+B)&(~A))+((A+B)&(~B))	Phoenix
26	(A + B) & (~C)	58	(~C) & (B + A)	Skoolgirl
73	(B) & (~B)	1	()	Poovey
19	((~B) & C) & B	88	Ø	joojoo
16	((~B) & (~C)) & (B & (~A))	17	((~B) & (~C)) & (B & C)	BassLady
70	B + (~B)	80	U	CenterField
68	B	7	(( ~A ) + B ) & B	Dirtybird
61	A+(A&B)	59	A	Pringle
40	(B & (~C)) & ((~B) & (~A))	88	Ø	David
6	((~A) + (~B)) & (~C))	11	((~A) & (~C)) + ((~B) & (~C))	Draco
68	B	27	(A+B) &  B	? Spartan same as Boki's
54	(-B) + (-C)	86	-(B&C)	PAC
7	((~A)+B)&B	74	B & B	Tiger

39	(B+C)&(C+B)	43	(B&C)&(B+C)	?Golfgirl
17	((~B) & (~C)) & (B & C)	88	Ø	Catseyes
1	()	88	Ø	DEUCE
1	()	16	((~B)&(~C))&(B&(~A))	Bubba
50	(~A) + B	68	B	?SunSport
37	(A&B)+B	68	B	Capricorn
16	((~B)&(~C))&(B&(~A))	17	((~B) & (~C)) & (B & C)	Rockclimber
27	(A+B) &  B	37	(A&B)+B	Rockclimber
23	(A+B) & (A+C)	63	A+ (B & C)	TBIRD
7	((~A) + B) & B	27	(A+B) &  B	Taurus
17	((~B) & (~C)) & (B & C)	19	((~B) & C) & B	Spartan
39	(B+C)&(C+B)	69	B+(C+B)	lexiowen

 

 Add rows to the table when needed.
? Marks means incorrect.
Correct the wrong ones 
and put a * next to your alias.

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NUMBER PROPERTIES

Listed below are the properties of numbers that we learned long ago in algebra class.
We apply the operations of addition (+) and multiplication (x) to numbers a, b, and c like this:

1. COMMUTATIVITY
a + b = b + a
3 + 4 = 4 + 3 = 7

a x b = b x a
3 x 4 = 4 x 3 = 12

2. ASSOCIATIVITY
(a + b) + c = a + (b + c)
(2 + 3) + 4 = 2 + (3 + 4) = 9

(a x b) x c = a x (b x c)
(2 x 3) x 4 = 2 x (3 x 4) = 24

3. IDENTITY
a + 0 = a
5 + 0 = 5

a x 1 = a
5 x 1 = 5

4. INVERSE
a + (-a) = 0
3 + (-3) = 0

a x 1/a = 1
3 x 1/3 = 1

5. DISTRIBUTION
a x (b + c) = a x b + a x c
2 x (3 + 4) = 2 x 3 + 2 x 4 = 14

a + (b x c) = (a + b) x (a + c)
2 + (3 x 4) = (2 + 3) x (2 + 4)
14 = 30 ?

That last distribution does not work out right. 14 does not equal 30.
But the first 4 properties are true for both addition and multiplication.
Now we ask you, do these properties apply to sets also? Continue...

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SET PROPERTIES

In the examples below, the operations of union (+) and intersection (&) are verified for properties 1 thru 4 using sets A, B, and C. For practice, use the Set Matching applet above to verify properties 1 thru 4 with your alphasets A B C. To view results in the applet, click inside an entry box in the applet, and then press the [Enter] key. The applet will print in red the items represented by the left statement and right statement. You can click the SORT SETS button to more easily check the left side against the right side. In the applet, use U or 1 for the Universal set U, and the letter O or zero 0 for the nonexistent empty set Ø.


A = {GEORWBUSH}
B = {NEWHAVCOTIU}
C = {SATURDYJL6194}


1. COMMUTATIVITY
Is + with sets commutative?
Does A + B = B + A ?

{GEORWBUSH} + {NEWHAVCOTIU} = {GEORWBUSHNAVCTI} = {NEWHAVCOTIUGRBS} = {NEWHAVCOTIU} + {GEORWBUSH}
YES


Is & with sets commutative?
Does A & B = B & A ?

{GEORWBUSH} & {NEWHAVCOTIU} = {EOWUH} = {NEWHAVCOTIU} & {GEORWBUSH}
YES


2. ASSOCIATIVITY
Is + with sets associative?
Does (A + B) + C = A + (B + C) ?

{GEORWBUSHNAVCTI} + {SATURDYJL6194} = {GEORWBUSHNAVCTITDYJL6194} = {GEORWBUSH} + {NEWHAVCOTIUSTRDYJL6194}
YES


Is & with sets associative?
Does (A & B) & C = A & (B & C) ?

{EOWUH} & {SATURDYJL6194} = {U} = {GEORWBUSH} & {ATU}
YES


3. IDENTITY
Is there an identity set for + ?
If so, what is it? A + ? = A

{GEORWBUSH} + { } = {GEORWBUSH} + Ø = {GEORWBUSH}
YES


Is there an identity set for & ?
If so, what is it? A & ? = A

{GEORWBUSH} & {ABCDEFGHIJKLMNOPQRSTUVWXYZ1234567890} = {GEORWBUSH} & U = {GEORWBUSH}
YES


4. INVERSE
Is there an inverse set for each set
so that A + ? = U ?

{GEORWBUSH} + {ACDFIJKLMNPQTVXYZ1234567890} = {ABCDEFGHIJKLMNOPQRSTUVWXYZ1234567890} = A + –A = U
YES


Is there an inverse set for each set
so that A & ? = Ø ?

{GEORWBUSH} & {ACDFIJKLMNPQTVXYZ1234567890} = A & –A = Ø
YES



USE THE SET MATCHER APPLET ABOVE TO VERIFY OR FALSIFY PROPERTY 5.

5. DISTRIBUTION
Is + with sets distributive?
Does A + (B & C) = (A + B) & (A + C)

Is & with sets distributive?
Does A & (B + C) = (A & B) + (A & C)

Click here for a Set Matcher Demo.

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ASSIGNMENT – & +

Listed below are some statements that need matching. For 4 points, find one pair of matching statements that no one else has posted, and post them to the table on the wiki. In other words, find one pair of equal statements. Copy to the wiki the left and right matching statements only. First come, first served. This table will become a reference page for future asignments—so be careful with your posting. I expect you to police this table and correct any wrong entries. Others will rely upon your accuracy. Remember, you will obtain wrong results if you do not use parentheses correctly. So check both left and right sides of your output boxes. See if they make sense before you post your matched set.

Footnote: To make typing in the applet easier,
you can substitute the symbols ~ ^ | respectively for – & + .

1. ( )
2. ((A + B) & ~C) & B
3. (~A + ~B) & (~B + ~C)
4. (~A + ~B) & ~B
5. (~A + ~B) & ~C
6. (~A + B) & B
7. (~A + ~C) & (~B + ~C)
8. (~A & ~B) + ~B
9. (~A & ~B) + ~C
10. (~A & ~C) + (~B & ~C)
11. (~A & B) + ~(A + B)
12. ~A + ~B
13. (~B & ~C) + (~A & ~B)
14. (~B & ~C) + (~B + C)
15. (~B & ~C) & (B & ~A)
16. (~B & ~C) & (B & C)
17. (~B & C) & A
18. (~B & C) & B
19. (~C & ~B) & ~C
20. (A + ~B) & (B + ~A)
21. (A + B) & (~A + ~B)
22. (A + B) & (A + C)
23. (A + B) & ~(A & B)
24. (A + B) & ~B
25. (A + B) & ~C
26. (A + B) & B
27. (A + C) & ~(~A & B)
28. (A + C) & (~B + C)
29. (A + C) & ~(B + C)
30. (A & ~B) + (B & ~A)
31. (A & ~B) & (B & ~A)
32. (A & ~C) + (B & (~C))
33. (A & B ) + ~(A + B)
34. (A & B) + (A & C)
35. (A & B) + ~A + B
36. (A & B) + ~B
37. (A & B) + B
38. (B + ~C) & (B & C)
39. (B + C) & (C + B)
40. (B & ~C) & (~B & ~A)
41. (B & ~C) & (B & A)
42. (B & ~C) & B
43. (B & C) & (B + C)
44. (C + ~B) + ~C
45. (C + B) & ~A
46. (C & ~B) + A
47. ~(A & C) & ~(B & C)
48. ~A + ~B
49. ~A + ~B + ~C
50. ~A + B
51. ~A & ~B
52. ~A & ~B & ~C
53. ~B + (~C & ~B)
54. ~B + ~C
55. ~B & (C & A)
56. ~B & C
57. ~C & (~B + C)
58. ~C & (B + A)
59. ~~~C
60. A
61. A + (~B & ~C)
62. A + (A & B)
63. A + (B & ~C)
64. A + (B & C)
65. A & (~B + ~C)
66. A & (A + B)
67. A & (B + C)
68. A & (B & ~C)
69. ((A + B) & ~A) + ((A + B) & ~B)
70. ((A + B) & ~A) & ((A + B) & ~B)
71. ((A & B) + ~A) + ((A & B) + ~B)
72. ((A & B) + ~A) & ((A & B) + ~B)
73. B
74. B + (C + B)
75. B + ~B
76. B + ~C
77. B & (~A & ~C)
78. B & ~B
79. B & B
80. B & ~(~A & C)
81. C
82. C + C
83. C & (B & C)
84. O
85. U
86. ~A
87. ~B
88. ~C
89. ~((A & C) + (B & C))
90. ~(A + B + C)
91. ~(A + B)
92. ~(A & B & C)
93. ~(A & B)
94. ~(B & C)
95. ~~A
96. Ø

Comments:

From wHolt - 12/8/06 11:15 AM

From wHolt - 9/29/06 12:34 PM

From wHolt - 9/29/06 12:27 PM

From wHolt - 9/16/06 12:03 PM

From wHolt - 9/16/06 12:04 AM