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Unformatted text preview: M42 — Discrete Mathematics Spring 2011 M. Stanley Sample First Exam Do not use any aids (calculators, computers, notes, etc.) on this exam. When asked to provide proofs, be sure to give careful, detailed and complete explanations in full English sentences. Form is as important as content. (1) ( 1 point each ) Let A = { 1 , 2 } and B = { 2 , 3 } . Let the universal set U = { 1 , 2 , 3 , 4 } . Find (a) A ∪ B = { 1 , 2 , 3 } (b) A ∩ B = { 2 } (c) A ⊕ B = { 1 , 3 } (d) A × B = { (1 , 2) , (1 , 3) , (2 , 2) , (2 , 3) } (e) P ( A ) = {∅ , { 1 } , { 2 } , { 1 , 2 }} (f) A \ B = { 1 } = { 2 , 3 , 4 } (2) ( 3 points ) Use a truth table to show that (( p ∨ ¬ q ) → q ) ≡ q . Answer: p q ¬ q p ∨ ¬ q ( p ∨ ¬ q ) → q T T F T T T F T T F F T F F T F F T T F Because the pattern of T ’s and F ’s in the q column and the ( p ∨¬ q ) → q column match, these two formulas are logically equivalent....
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This note was uploaded on 03/13/2012 for the course MATE 153 taught by Professor Staff during the Fall '08 term at San Jose State University .
 Fall '08
 Staff

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