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Unformatted text preview: CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE AND SOFTWARE ENGINEERING COMP232 MATHEMATICS FOR COMPUTER SCIENCE ASSIGNMENT 2 FALL 2010 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 counterexample. parenleftBig xP ( x ) parenrightBig parenleftBig xQ ( x ) parenrightBig x y parenleftBig P ( x ) Q ( y ) parenrightBig 2. Prove that [( p q ) ( p s ) ( q t )] s t , using a direct proof (with cases). 3. Prove that [( p q ) ( p s ) ( q t )] s t , using a proof by contradiction. 4. Prove that [( p q ) ( p s ) ( q t )] s t , by proving the contrapositive.by proving the contrapositive....
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- Fall '10