Question:
If the truth value of the statement $\mathrm{P} \rightarrow(\sim \mathrm{p} \vee \mathrm{r})$ is false $(\mathrm{F})$, then the truth values of the statements $\mathrm{p}, \mathrm{q}, \mathrm{r}$ are respectively :
Correct Option: , 3
Solution:
$\mathrm{P} \rightarrow(\sim \mathrm{q} \vee \mathrm{r})$
$\sim \mathrm{p} \vee(\sim \mathrm{q} \vee \mathrm{r})$
$\left.\left.\begin{array}{l}\sim \mathrm{p} \rightarrow \mathrm{F} \\ \sim \mathrm{q} \rightarrow \mathrm{F} \\ \mathrm{r} \rightarrow \mathrm{F}\end{array}\right\} \Rightarrow \begin{array}{l}\mathrm{p} \rightarrow \mathrm{T} \\ \mathrm{q} \rightarrow \mathrm{T} \\ \mathrm{r} \rightarrow \mathrm{F}\end{array}\right\}$