Answer
The logical connective $\leftrightarrow$, or "if and only if" evaluates to true if the propositions on each side of the connective have the same truth value. In the case of both $\neg p\leftrightarrow \neg q$ and $p\leftrightarrow q$, both $p$ and $q$ would have to be false, or both $p$ and $q$ would have to be true in order for the propositions on each side of the arrow to have the truth value. This means that the propositions evaluate to the same truth values for all values of $p$ and $q$, and so they are equivalent.
Work Step by Step
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