# test1_key - COT 3100-01 Feb 142001 Test#1(100 pts Solutions...

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COT 3100-01 Feb. 14’2001 Test#1 (100 pts) Solutions Name:_________________ SSN:__________________ 1. For each of the Venn diagrams write the set represented by shaded area in terms of set operations on sets A , B and C . Try to simplify your answer to as few symbols as you can. a) (4pts) Ans: A B - C b) (4pts). Ans: B C - A C c) (4pts) Ans. ( B C ) - ( B C ) 1 A B C A B C A B C

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2. (8pts). Use truth table method to determine whether the following statement is a tautology, contradiction, or neither: [ p ( q ∨¬ r )] ( ¬ p r ) p q r ¬ p ¬ r q ∨¬ r p ( q ∨¬ r ) ¬ p r [ p ( q ∨¬ r )] ( ¬ p r ) 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 (where 1 stands for True and 0 for False) Since we have True in all rows of the last column, the statement [ p ( q ∨¬ r )] ( ¬ p r ) is a tautology. 3. (10pts). Use laws of logic to prove that ( p r ) ( q r ) is equivalent to ( p q ) r . Use one law at a step (except commutative and associative laws). Specify exactly what you do at each step. ( p
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test1_key - COT 3100-01 Feb 142001 Test#1(100 pts Solutions...

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