Answer
$\begin{array}{llllll}
p & q & \sim p & \sim q & p\wedge\sim q & \sim p\vee( p\wedge\sim q)\\
\hline T & T & F & F & F & F\\
T & F & F & T & T & T\\
F & T & T & F & F & T\\
F & F & T & T & F & T
\end{array}$
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
$\sim p\wedge\sim q$ and the conjunction truth table,
(true only when both inputs are true)
$\begin{array}{llllll}
p & q & \sim p & \sim q & p\wedge\sim q & \\
\hline T & T & F & F & F & \\
T & F & F & T & T & \\
F & T & T & F & F & \\
F & F & T & T & F &
\end{array}$
Finally, for $\sim p\vee( p\wedge\sim q)$,
use disjunction truth table on inputs from columns 3 and 5
(true if at least one input is true)
$\begin{array}{llllll}
p & q & \sim p & \sim q & p\wedge\sim q & \sim p\vee( p\wedge\sim q)\\
\hline T & T & F & F & F & F\\
T & F & F & T & T & T\\
F & T & T & F & F & T\\
F & F & T & T & F & T
\end{array}$