Answer
$\begin{array}{llllll}
p & q & r & \sim q & \sim q\vee r & p\wedge(\sim q\vee r)\\
\hline T & T & T & F & T & T\\
T & T & F & F & F & F\\
T & F & T & T & T & T\\
T & F & F & T & T & T\\
F & T & T & F & T & F\\
F & T & F & F & F & F\\
F & F & T & T & T & F\\
F & F & F & T & T & F
\end{array}$
Work Step by Step
Set up a truth table for three inputs, p,q and r:
$\begin{array}{lllll}
p & q & r & ... & \\
\hline T & T & T & & \\
T & T & F & & \\
T & F & T & & \\
T & F & F & & \\
F & T & T & & \\
F & T & F & & \\
F & F & T & & \\
F & F & F & &
\end{array}$
Next column: $\sim q$,
negation of column 2:
$\begin{array}{lllll}
p & q & r & \sim q & \\
\hline T & T & T & F & \\
T & T & F & F & \\
T & F & T & T & \\
T & F & F & T & \\
F & T & T & F & \\
F & T & F & F & \\
F & F & T & T & \\
F & F & F & T &
\end{array}$
Next column: $\sim q\vee r,$
disjunction, inputs from columns 3 and 4:
$\begin{array}{lllllll}
p & q & r & \sim q & \sim q\vee r & & \\
\hline T & T & T & F & T & & \\
T & T & F & F & F & & \\
T & F & T & T & T & & \\
T & F & F & T & T & & \\
F & T & T & F & T & & \\
F & T & F & F & F & & \\
F & F & T & T & T & & \\
F & F & F & T & T & &
\end{array}$
Final column: $p\wedge(\sim q\vee r),$
conjunction, inputs from columns 1 and 5:
$\begin{array}{llllll}
p & q & r & \sim q & \sim q\vee r & p\wedge(\sim q\vee r)\\
\hline T & T & T & F & T & T\\
T & T & F & F & F & F\\
T & F & T & T & T & T\\
T & F & F & T & T & T\\
F & T & T & F & T & F\\
F & T & F & F & F & F\\
F & F & T & T & T & F\\
F & F & F & T & T & F
\end{array}$
