Construct a truth table for the statement.
-$\sim \mathrm{r} \wedge \sim \mathrm{p}$
A)
$\begin{array}{ccc}
\mathrm{r} & \mathrm{p} & (\sim \mathrm{r} \wedge \sim \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$
B)
$\begin{array}{ccc}
\mathrm{r} & \mathrm{p} & (\sim \mathrm{r} \wedge \sim \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$
C)
$\begin{array}{ccc}
\mathrm{r} & \mathrm{p} & (\sim \mathrm{r} \wedge \sim \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$
D)
$\begin{array}{ccc}
\mathrm{r} & \mathrm{p} & (\sim \mathrm{r} \wedge \sim \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$

Question

Quizplus · Accepted Answer

The correct truth table for $\sim \mathrm{r} \wedge \sim \mathrm{p}$ shows that the statement is true only when both r and p are false. The AND operation ($\wedge$) requires both conditions to be true for the result to be true; since we are negating both r and p, the only case where the statement is true is when both r and p are false.

Construct a Truth Table for the Statement ∼r∧∼p\sim \mathrm{r} \wedge \sim \mathrm{p}∼r∧∼p

Construct a Truth Table for the Statement $\sim \mathrm{r} \wedge \sim \mathrm{p}$