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