Answer
See step by step work for solution.
Work Step by Step
a) $p \to \neg q$
\begin{array}{c|c|c}
p & q & p \to \neg q& \\
T & T & F \\
T & F & T \\
F & T & T \\
F & F & T \\
\end{array}
b) $\neg p \leftrightarrow q$
\begin{array}{c|c|c}
p & q & \neg p \leftrightarrow q& \\
T & T & F \\
T & F & T \\
F & T & T \\
F & F & F \\
\end{array}
c) $(p \to q) \lor (\neg p \to q)$
\begin{array}{c|c|c}
p & q & p \to q & \neg p \to q& (p \to q) \lor (\neg p \to q) \\
T & T & T&T &T \\
T & F & F&T &T\\
F & T & T& T &T\\
F & F & T& F&T\\
\end{array}
d)$(p \to q) \land (\neg p \to q)$
\begin{array}{c|c|c}
p & q & p \to q & \neg p \to q& (p \to q) \land (\neg p \to q) \\
T & T & T&T &T \\
T & F & F&T &F\\
F & T & T& T &T\\
F & F & T& F&F\\
\end{array}
e)$(p \leftrightarrow q) \lor (\neg p \leftrightarrow q)$
\begin{array}{c|c|c}
p & q & p \leftrightarrow q &\neg p \leftrightarrow q& (p \leftrightarrow q) \lor (\neg p \leftrightarrow q) \\
T & T & T&F &T \\
T & F & F&T &T\\
F & T & F& T &T\\
F & F & T& F&T\\
\end{array}
f)$(\neg p \leftrightarrow \neg q) \leftrightarrow ( p \leftrightarrow q)$
\begin{array}{c|c|c}
p & q & \neg p \leftrightarrow \neg q &p \leftrightarrow q& (\neg p \leftrightarrow \neg q) \leftrightarrow ( p \leftrightarrow q) \\
T & T & T&T &T \\
T & F & F&F &T\\
F & T & F& F &T\\
F & F & T& T&T\\
\end{array}
