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#2.5.8. 10, Jr. 16, 19.25, 36 (pages 53-55). Supplement S1 . Give a counterexample to show that Vx(P(x) → Q(x)) and YxP(x) → YxQ(x) may not be logically equivalent.

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Answer #1

The first statement implies the second one. So in order to look for a counter example, we must look for P(X) and Q(X) such that the second statement is satisfied but not first. The following example works:

uncfton. ler p(T) be the Statement รุ่r) o R a) be the statement Cz) lo) and This impes that Ht i a conktant Juncfon not e tnue as t*) na^

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