Question
Determine whether $\forall x(P(x) \leftrightarrow Q(x))$ and $\forall x P(x) \leftrightarrow$ $\forall x Q(x)$ are logically equivalent. Justify your answer.
Step 1
Step 1: Let's consider a domain for $x$, and let's say that $P(a)$ is false but $Q(a)$ is true, and $P(b)$ is true but $Q(b)$ is false. Show more…
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Determine whether $\forall x(P(x) \rightarrow Q(x))$ and $\forall x P(x) \rightarrow$ $\forall x Q(x)$ are logically equivalent. Justify your answer.
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