CS 336 PreTest_sets_1_solutions

CS 336 PreTest_sets_1_solutions - CS 336 Pre-Test 1...

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CS 336 Pre-Test 1 Solutions Logic 1. Sentential Calculus (SC) 1.1* Prove that for all propositions p , q , and r : a) [~q ~p] [p q] Consider the following truth table: p q ~ q ~ p ~ ~ q p p q [~ ~ ] [ ] q p p q F F T T T T T F T F T T T T T F T F F F T T T F F T T T b) [p (q r)] [~p (q r)] Consider the following truth table: p q r q r ( ) p q r ~ p ~ p q r [ ( )] [~ ] p q r p q r ∨ ∨ F F F F T T T T F F T F T T T T F T F F T T T T F T T T T T T T T F F F F F F T T F T F T F T T T T F F T F T T T T T T T F T T 2. First Order Predicate Calculus (PC) 2.1.* State an assertion that, if true, would falsify each of the following claims: a) All zamzows have tenockritus. “A is a zamzow but does not have tenockritus.” b) Some zamzows have tenockritus. “There exist no zamzow that has tenockritus.”

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2.2. Given the following two axioms: 2200 x Px Qx 5 x ~Qx ~Rx Prove that y ~Py From the second assumption we have some element a so that ~ ~ Qa Rx . This implies that ~ Qa . If Pa were true then from the first assumption we could conclude Qa , but that contradicts ~ Qa . We coclude that ~ Pa , and thus
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CS 336 PreTest_sets_1_solutions - CS 336 Pre-Test 1...

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