Answer
The columns in the truth table for $\neg(p\leftrightarrow q)$ and $\neg p\leftrightarrow q$
are identical, so the statements are logically equivalent.
Work Step by Step
$\left[\begin{array}{ccccc}
p & q & p\leftrightarrow q & \neg(p\leftrightarrow q)\\
\hline & & & \\
T & T & T & F\\
T & F & F & T\\
F & T & F & T\\
F & F & T & F
\end{array}\right.\left[\begin{array}{cc}
\neg p & \neg p\leftrightarrow q\\
\hline & \\
F & F\\
F & T\\
T & T\\
T & F
\end{array}\right]$
The columns in the truth table for $\neg(p\leftrightarrow q)$ and $\neg p\leftrightarrow q$
are identical, so the statements are logically equivalent.
