Consider the following quantified propositions over an arbitrary domain: A: 3x(P(x) Q(x)) B: VxP(x)yQ(y) a. (5...

 

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Consider the following quantified propositions over an arbitrary domain: A: 3x(P(x)→ Q(x)) B: VxP(x)→yQ(y) a. (5 points) Prove that A⇒B. b. (10 points) Prove that B⇒A. For both parts use only the laws of propositional logic and the rules of inference, indicating which law or rule is used at each step. Consider the following quantified propositions over an arbitrary domain: A: 3x(P(x)→ Q(x)) B: VxP(x)→yQ(y) a. (5 points) Prove that A⇒B. b. (10 points) Prove that B⇒A. For both parts use only the laws of propositional logic and the rules of inference, indicating which law or rule is used at each step.

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