COT 3100 Section 2 Homework #2 Spring 2000 Solutions
1)
a)
{0,1}
b)
{0,1,6,12}
c)
{0,6,24}
2)
a)
128
b)
127
c)
127
d)
126
e)
7
C
3
= 35
f)
2
5
, or 32
g)
5
C
3
= 10
h)
64
i)
64
3)
Given that our universe U has 20 elements(U = 20) and that A, B and C are sets such
that A = 10, B = 12, C = 8, (A
∩
B)
∩
C = 4, A
∩
B = 7, and (A
∪
B)
∪
C=18,
find the following values. Please show your work. (Note: if the values can not be
determined given the information above, state this and give two examples(by use of a
Venn Diagram) where the size of the set in question is different, but all of the above
properties hold.)
a)
U – ((A
∪
B)
∪
C) = 2
b)
U – (A
∩
(B
∩
C)) = 16
c)
A
∩
C can not be determined. In particular, this value could be either 0 or 1 and
still be consistent with the data given.
d)
A
∪
B = 15 by inclusionexclusion principle
e)
(C – A) – B = 3, using answer from d with given info about (A
∪
B)
∪
C.
4)
Question #14 on page 138 of the text. Here it is:
How many subsets of {1,2,3,...,11} contain at least one even integer?
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 Spring '09
 Empty set, Natural number

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