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2. [15 pts] Which of the following pairs of expressions are logically equivalent? Prove your answer. 1. x(P(x)Q(x)) and xP(x)xQ(x). 2. x(P(x)Q(x)) and xP(x)xQ(x). 3.

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2. [15 pts] Which of the following pairs of expressions are logically equivalent? Prove your answer. 1. x(P(x)Q(x)) and xP(x)xQ(x). 2. x(P(x)Q(x)) and xP(x)xQ(x). 3. xP(x)xQ(x) and xy(P(x)Q(y)) (here all quantifiers have the same nonempty domain)

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