Answer
$a.$
$\left[\begin{array}{ll}
p & q\\
\hline & \\
T & T\\
T & F\\
F & T\\
F & F
\end{array}\right. \begin{array}{l}
p\wedge q\\
\hline\\
T\\
F\\
F\\
F
\end{array} \left.\begin{array}{l}
p\vee(p\wedge q)\\
\hline\\
T\\
T\\
F\\
F
\end{array}\right]$
$b.$
$\left[\begin{array}{ll}
p & q\\
\hline & \\
T & T\\
T & F\\
F & T\\
F & F
\end{array}\right. \begin{array}{l}
p\vee q\\
\hline\\
T\\
T\\
T\\
F
\end{array} \left.\begin{array}{l}
p\wedge(p\vee q)\\
\hline\\
T\\
T\\
F\\
F
\end{array}\right]$
Work Step by Step
$ a.\qquad$The columns for $p\vee(p\wedge q)$ and $p$ are identical.
$ b.\qquad$The columns for $p\wedge(p\vee q)$ and $ p $ are identical.
