Answer
$\begin{array}{llllll}
p & q & \sim p & \sim q & p\vee\sim q & \sim p\wedge( p\vee\sim q)\\
\hline T & T & F & F & T & F\\
T & F & F & T & T & F\\
F & T & T & F & F & F\\
F & F & T & T & T & T
\end{array}$
Work Step by Step
Set up a truth table for two inputs, p and q:
$\begin{array}{llll}
p & q & ... & ...\\
\hline T & T & & \\
T & F & & \\
F & T & & \\
F & F & &
\end{array}$
In columns 3 and 4, use the negation table for $\sim p$ and $\sim q$
$\begin{array}{llllll}
p & q & \sim p & \sim q & & \\
\hline T & T & F & F & & \\
T & F & F & T & & \\
F & T & T & F & & \\
F & F & T & T & &
\end{array}$
In the next column (5th) use inputs from columns 1 and 4 for
$p\vee\sim q$ and the disjunction truth table,
(true if any of the inputs are true)
$\begin{array}{llllll}
p & q & \sim p & \sim q & p\vee\sim q & \\
\hline T & T & F & F & T & \\
T & F & F & T & T & \\
F & T & T & F & F & \\
F & F & T & T & T &
\end{array}$
Finally, for $\sim p\wedge( p\vee\sim q)$,
use conjunction truth table on inputs from columns 3 and 5
(true only if both inputs are true)
$\begin{array}{llllll}
p & q & \sim p & \sim q & p\vee\sim q & \sim p\wedge( p\vee\sim q)\\
\hline T & T & F & F & T & F\\
T & F & F & T & T & F\\
F & T & T & F & F & F\\
F & F & T & T & T & T
\end{array}$
