assignment_1 - CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER...

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Unformatted text preview: CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE AND SOFTWARE ENGINEERING COMP232 MATHEMATICS FOR COMPUTER SCIENCE ASSIGNMENT 1 FALL 2011 Due Date: Thursday September 29 at midnight 1. Use truth tables to determine whether each of the following statements is a tautology, a contradiction, or a contingency , that is, neither a tautology nor a contradiction. (a) p ∨ ( q ∧ r ) ↔ ( p ∨ q ) ∧ ( p ∨ r ) (b) p ∧ ¬ ( q → p ) (c) ( ¬ p ∧ ( p ∨ q )) → q (d) (( p → r ) ∨ ( q → r )) ↔ (( p ∨ q ) → r ) 2. Prove the following logical equivalences without using truth tables. (a) ( ¬ p ) → ( q → r ) ≡ q → ( p ∨ r ) (b) ( p → r ) ∨ ( q → r ) ≡ (( p ∧ q ) → r ) (c) ( p → q ) ∧ ( p → r ) ≡ ( p → ( q ∧ r )) (d) (( p ∨ q ) ∧ ( ¬ p ∨ r )) → ( q ∨ r ) ≡ T 3. Write down the negations of each of the following statements in their simplest form ( i.e. , do not simply state ”It is not the case that...”). Below, x denotes an integer,...
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assignment_1 - CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER...

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