COT3100C-01, Fall 2002 Assigned: 9/10/2002 S. Lang Assignment #2 (40 pts.) Due: 9/19 in class by 8:45 am 1. (10 pts.) 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.) 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)
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