Answer
$\begin{array}{lllllll}
p & q & r & \sim p & \sim q & r\wedge\sim p & (r\wedge\sim p)\vee\sim q\\
\hline T & T & T & F & F & F & F\\
T & T & F & F & F & F & F\\
T & F & T & F & T & T & T\\
T & F & F & F & T & F & T\\
F & T & T & T & F & T & T\\
F & T & F & T & F & F & F\\
F & F & T & T & T & T & T\\
F & F & F & T & T & F & T
\end{array}$
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 two columns: $\sim p$ and $\sim q$,
negation of columns 1 and 2:
$\begin{array}{lllllll}
p & q & r & \sim p & \sim q & & \\
\hline T & T & T & F & F & & \\
T & T & F & F & F & & \\
T & F & T & F & T & & \\
T & F & F & F & T & & \\
F & T & T & T & F & & \\
F & T & F & T & F & & \\
F & F & T & T & T & & \\
F & F & F & T & T & &
\end{array}$
Next column: $r\wedge\sim p$,
conjunction of columns 3 and 4:
$\begin{array}{lllllll}
p & q & r & \sim p & \sim q & r\wedge\sim p & \\
\hline T & T & T & F & F & F & \\
T & T & F & F & F & F & \\
T & F & T & F & T & T & \\
T & F & F & F & T & F & \\
F & T & T & T & F & T & \\
F & T & F & T & F & F & \\
F & F & T & T & T & T & \\
F & F & F & T & T & F &
\end{array}$
Final column: $(r\wedge\sim p)\vee\sim q$,
disjunction of columns 6 and 5:
$\begin{array}{lllllll}
p & q & r & \sim p & \sim q & r\wedge\sim p & (r\wedge\sim p)\vee\sim q\\
\hline T & T & T & F & F & F & F\\
T & T & F & F & F & F & F\\
T & F & T & F & T & T & T\\
T & F & F & F & T & F & T\\
F & T & T & T & F & T & T\\
F & T & F & T & F & F & F\\
F & F & T & T & T & T & T\\
F & F & F & T & T & F & T
\end{array}$
