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# Hmk2sol - COT 3100 Section 2 Homework#2 Spring 2000...

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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 inclusion-exclusion 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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