Question:
Let $\mathrm{p}, \mathrm{q}, \mathrm{r}$ be three statements such that the truth value of $(p \wedge q) \rightarrow(\sim q \vee r)$ is $F$. Then the truth values of $\mathrm{p}, \mathrm{q}, \mathrm{r}$ are respectively :
Correct Option: , 3
Solution:
$(\mathrm{p} \wedge \mathrm{q}) \rightarrow(\sim \mathrm{q} \vee \mathrm{r})=$ false
when $(p \wedge q)=T$
and $(\sim \mathrm{q} \vee \mathrm{r})=\mathrm{F}$
So $(p \wedge q)=T$ is possible when $p=q=$ true
$\therefore \quad \sim \mathrm{q}=$ False $(\mathrm{q}=$ true $)$
So $(\sim \mathrm{q} \vee \mathrm{r})=$ False is possible if $\mathrm{r}$ is false
$\therefore \mathrm{p}=\mathrm{T}, \mathrm{q}=\mathrm{T}, \mathrm{r}=\mathrm{F}$