# key2fa02 - COT3100C-01 Fall 2002 S Lang Solution Keys to...

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COT3100C-01, Fall 2002 S. Lang Solution Keys to Assignment #2 (40 pts.) 9/20/2002 1. (10 pts., 2 pts. each part) The following Venn diagram shows three sets A (red) , B (blue) , and C (green) contained within a universe set named U (violet) . In the diagram, different subsets (regions) are labeled by the numbers 1 through 8. Thus, set A contains subsets labeled 1, 2, 4, and 5; set B contains subsets labeled 2, 3, 5, and 6; set C contains subsets labeled 4, 5, 6, and 7; set U contains subsets labeled 1 through 8 (i.e., the universe). Now, give the labels (i.e., numbers) of all the subsets that are contained in each of the following sets: 2. (24 pts., 4 pts. each part) Prove each of the following statements (a) – (f), assuming the symbols A , B , and C represent sets contained in a universe set U . You are allowed to use appropriate definitions, and the following theorems and laws ( but only these ) in the proof. Be sure to explain each step of your proof . (Commutative Law) A B = B A , A B = B A . (Associative Law) ( A B ) C = A ( B C ), ( A B ) C = A ( B C ). (Distributive Law) A ( B C ) = ( A B ) ( A C ), A ( B C ) = ( A B ) ( A C ). (Idempotent Law) A A = A , A A = A . (Absorption Law) A ( A B ) = A , A ( A B ) = A . In particular, A U = A , and A U = U , where U denotes the universe. (De Morgan’s Law)

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key2fa02 - COT3100C-01 Fall 2002 S Lang Solution Keys to...

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