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