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