If $\mathrm{p} \rightarrow(\sim \mathrm{p} \vee \sim \mathrm{q})$ is false, then the truth values of $p$ and…
If $\mathrm{p} \rightarrow(\sim \mathrm{p} \vee \sim \mathrm{q})$ is false, then the truth values of $p$ and $q$ are respectively
F, F
$\mathrm{F}, \mathrm{T}$
$\mathrm{T}, \mathrm{T}$
$\mathrm{T}, \mathrm{F}$
Solution
- Consider option (C)
$\begin{aligned}
& p \rightarrow(\sim p \vee \sim q) \\
& \equiv T \rightarrow(\sim T \vee \sim T) \\
& \equiv T \rightarrow(F \vee F) \\
& \equiv T \rightarrow F \\
& \equiv F
\end{aligned}$
$\therefore \quad$ Option (C) is the correct answer.