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Unformatted text preview: Name _____________________ Right Left CS 336 Pre-Test 1 Logic 1. Sentential Calculus (SC) 1.1* Prove that for all propositions p , q , and r : a) [~q ⇒ ~p] ⇒ [p ⇒ q] b) [p ⇒ (q ∧ r)] ⇒ [~p ∨ (q ∨ r)] 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. b) Some zamzows have tenockritus. 2.2. Given the following two axioms: 2200 x Px ⇒ Qx 5 x ~Qx ∧ ~Rx Prove that 5 y ~Py 2.3. Consider the predicates Wx ( x is a woman), CHILDOFxy ( y is a child of x ), and Mx ( x is a mother). a) * Write a PC formula to describe the fact that all women with children are mothers. b) Modify the definition of mother given in (a) to add the fact that only women with children are mothers. Use this, plus the fact that Mary has no children, to prove children are mothers....
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