Quiz2Sol - by adding 2 to each of the first 8 subsets....

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COT 3100 Quiz #2 – Sets Name : _______________ Date : 2/1/01 1) (4 pts) Let A= {1, 3, 5, 7, 9}, B= {1, {2, 3}, 4, 5}, C= {1, 2, 3, 4, }, and D={{5}, 6}. List the members of each of the following sets explicitly: a) A B = { 1, 3, 5, 7, 9, 4, {2,3} } b) A – B = { 3, 7, 9 } c) B D = { } d) A (C D) = { 1, 3 } 2) (3 pts) Let A = {2, 3, 5, 7, 11}. For any set X, let sum(X) denote the sum of the elements in the set. For how many different subsets Y of A is sum(Y) an odd number? Consider all the subsets of {3, 5, 7, 11}. The subsets X of odd cardinality all have sum(X) = odd number. There are 2 4-1 = 8 of these subsets total, using the formula given in class on 1/30. Now, we can create 8 more subsets X such that sum(X) = odd
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Unformatted text preview: by adding 2 to each of the first 8 subsets. Thus, the answer is 2x8 = 16. 3) (7 pts) A, B, C and D are sets such that A B and C D. Prove that (B C) (A D). We must show that (B C) (A D). Essentially, we need to show that if x (B C) then x (A D). To prove this, assume that x (B C). Under this assumption, we must show that x (A D). Using the defn of intersection, we find that x B and x C. Since C D, by the defn of subset we have that x D. But, we know by the defn of union, that x A D....
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This document was uploaded on 07/14/2011.

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