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COT 3100 Fall 2002 Homework #2 Solutions
1) a)
{0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
b)
{4,5}
c)
{0, 6, 24}
2)
a)
U – ((A
∪
B)
∪
C) = U  ((A
∪
B)
∪
C) = 50  40 = 10
b)
U – (A
∩
(B
∩
C)) = U  (A
∩
(B
∩
C)) = 50  7 = 43
c)
Can't be determined. Consider the two following situations described in the table
below:
A
B
C
Example #1
Example #2
0
0
0
10
10
0
0
1
8
8
0
1
0
3
4
0
1
1
5
4
1
0
0
4
3
1
0
1
4
5
1
1
0
9
9
1
1
1
7
7
To read this, each row on the table corresponds to the intersection of three sets.
For example, the row corresponding to 0, 1, 1 corresponds to the set
¬
A
∩
B
∩
C.
Each entry in the example columns signifies the number of elements in the set
designated by the row. These two examples show that A
∩
C could be 11 and could
be 12. Since both of these are possible, a definite answer can not be determined.
d)
A
∪
B = A + B  A
∩
B = 24 + 24  16 = 32
e)
(C – A) – B = ((A
∪
B)
∪
C)  A
∪
B = 40  32 = 8
3)
A
∪
( (A
∪
C)
∩
B
∩
¬
(
¬
A
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This document was uploaded on 07/14/2011.
 Spring '09

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