s-test1-1190-tan

# s-test1-1190-tan - 0.1 Midterm test Math 1190 S1...

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0.1. Midterm test Math 1190 S1 solutions (tan version). (1) (a) (10pts) Are the formulas p ≡ ¬ q and ( p ∨ ¬ q ) ( ¬ p q ) logically equivalent? Justify your answer. Solution. No. Via truthtable. (b) (10pts) Are the formulas ( p q ) r and p q r logically equiva- lent? Justify your answer. Solution. No. Via truthtable. (2) (18pts) Show that p q r and ( p r ) ( q r ) are logically equiva- lent without using truth tables. Instead you can use any of the formulas provided below. Solution. p q r ≡ ¬ ( p q ) r (1) ( ¬ p ∨¬ q ) r DeMorgan laws ( ¬ p r ) ( ¬ q r ) associativity and idempotent laws ( p r ) ( q r ) (1) Identity laws p T p p F p Domination laws p T T p F F Idempotent laws p p p p p p Double negation law ¬ ( ¬ p ) p Commutative laws p q q p p q q p Associative laws ( p q ) r p ( q r ) ( p q ) r p ( q r ) Distributive laws p ( q r ) ( p

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s-test1-1190-tan - 0.1 Midterm test Math 1190 S1...

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