# Hmk1sol - COT 3100 Homework#1 Section 2 Spring 2000...

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COT 3100 Homework#1 Section 2 Spring 2000 Solutions 1) p q r q ¬ r p (q ¬ r ) 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 1 Thus p (q ¬ r ) is true for the three truth assignments: p=1,q=0,r=0 p=1,q=1,r=0 p=1,q=1,r=1 2) p q r p q r (q p) (p q) ( r (q p)) 0 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 p q r p r 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 The left hand columns of both of these truth tables are equivalent, hence the expressions are as well.

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3) ( (p q) (r (q p)) ) ( ( ¬ p q) (r (q p)) ) Implication Identity ( ¬ ( ¬ p q) (r (q p)) ) Implication Identity ( ( ¬¬ p ¬ q) (r (q p)) ) De Morgan’s Law ( (p ¬ q) (r (q p)) ) Double Negation ( (p ¬ q) ((q p) r) ) Commutative Law ( ((p ¬ q) (q p)) r ) Associative Law ( ((p ¬ q) (p q)) r ) Commutative Law ( (p ( ¬ q
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Hmk1sol - COT 3100 Homework#1 Section 2 Spring 2000...

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