s09_t02_03

s09_t02_03 - UNIVERSITY OF WATERLOO School of Computer...

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UNIVERSITY OF WATERLOO School of Computer Science CS245 Logic and Computation Spring 2009 TUTORIALS 2 and 3 1. Transformational proof of ¬ ( p q ) ( ¬ p q ) WV ¬ p ¬ ( p q ) ( ¬ p q ) WV ( ¬ p ∧ ¬ q ) ( ¬ p q ) De Morgan WV ¬ p ( ¬ q q ) Distributive WV ¬ p true Excluded Middle WV ¬ p Simplification I 2. Transformational proof of p ( p q ) WV ( p q ) p ( p q ) WV p ( ¬ p q ) Implication WV ( p ∧ ¬ p ) ( p q ) Distributive WV false ( p q ) Contradiction WV p q Simplification I 1
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3. Transformational proof of ( p q ) WV (( p q ) ( p q )) (( p q ) ( p q )) WV (( p q ) ( p q )) (( p q ) ( p q )) Equivalence WV ( ¬ ( p q ) ( p q )) ( ¬ ( p q ) ( p q )) Implication (2 × ) WV ( ¬ p ∨ ¬ q p q ) ( ¬ ( p q ) ( p q )) De Morgan (*) WV ( ¬ p p ∨ ¬ q q ) ( ¬ ( p
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s09_t02_03 - UNIVERSITY OF WATERLOO School of Computer...

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