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Unformatted text preview: B ) ∪ C , A ∪ ( B ∩ C ) and A ∩ B , where X is the complement of X relative to U . Problem 4 (a) Let A be a set of size n . Prove that the power set P ( A ) of A has size 2 n . (b) Let B and C be sets with | C | = 2 . If there are 128 distinct functions from B to C , what is | B | ? Justify your answer. (c) Let D be a set of size n with n ≥ 2 . How many distinct reﬂexive and symmetric relations are there on D ? Justify your answer. Problem 5 Prove that if k is odd, then 2 n +2 divides k 2 n-1 for all positive integers n ....
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- Spring '10
- 1 Hour, Nanyang Technological University, Foundations of mathematics