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

Question

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

Quizplus · Accepted Answer

The expression $W \wedge \sim W$ is always false because $W$ and $\sim W$ (not $W$) are opposites and cannot both be true at the same time. Therefore, $W \vee (W \wedge \sim W)$ simplifies to $W \vee F$, which is just $W$. This means the truth value of the whole expression directly follows the truth value of $W$: true when $W$ is true, and false when $W$ is false.

Construct a Truth Table for the Statement W∨(W∧∼W)W \vee(W \wedge \sim W)W∨(W∧∼W)

Construct a Truth Table for the Statement $W \vee(W \wedge \sim W)$