Answer
The statement $\neg(p\leftrightarrow q)$ means "the opposite of p if and only if q". This statement evaluates to true only when $p$ and $q$ have the opposite truth value, so it is only true when $p$ is true and $q$ is false or $p$ is false and $q$ is true. The second proposition, $p\leftrightarrow\neg q$ means "p if and only if not q". This too will evaluate to true only when both $p$ and $q$ are have opposite truth values, as it is saying one if and only if not the other. Since the two propositions have the same truth value for every truth assignment of $p$ and $q$, they are logically equivalent.
Work Step by Step
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