assn2 - CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE...

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CONCORDIA UNIVERSITY COMP 232/2 Mathematics for Computer Science FALL 2010 Assignment 2 In each of the problems below it is especially important that your proof (or counter example) is correct, clear, complete, concise, and carefully presented, using proper mathematical notation. Points will be deducted if your presentation does not satisfy these requirements. 1. If the following equivalence is valid then give a proof. If the equivalence is invalid then give a counter example. ± x P ( x ) ² ± x Q ( x ) ² ≡ ∀ x y ± P ( x ) Q ( y ) ² 2. Prove that ± ( p q ) ( p s ) ( q t ) ² = s t using a direct proof (with cases). 3. Prove that ± ( p q ) ( p s ) ( q t ) ² = s t using a proof by contradiction. 4. Prove that ± ( p q ) ( p s ) ( q t ) ² = s t by proving the contrapositive. 5.
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This note was uploaded on 11/15/2010 for the course ENCS COMP 232 taught by Professor Ford during the Fall '10 term at Concordia CA.

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