If $(\sim \mathrm{p} \wedge \mathrm{q}) \rightarrow \mathrm{r}$ is false then the truth values of…
If $(\sim \mathrm{p} \wedge \mathrm{q}) \rightarrow \mathrm{r}$ is false then the truth values of $\mathrm{p}, \mathrm{q}, \mathrm{r}$ are respectively
$\mathbf{F}, \mathbf{T}, \mathbf{F}$
$\mathrm{F}, \mathrm{T}, \mathrm{T}$
$\mathrm{T}, \mathrm{T}, \mathrm{F}$
$\mathrm{F}, \mathrm{F}, \mathrm{T}$
Solution
Given $(\sim p \wedge q) \rightarrow r$ is false $T \rightarrow F \equiv F$
We know that $T \rightarrow F=F$
$\therefore \sim p \wedge q=T \quad$ and $r \equiv F$
Also we know that $\mathrm{T} \wedge \mathrm{T}=\mathrm{T}$
$\therefore \mathrm{q} \equiv \mathrm{T}$ and $\sim \mathrm{p}=\mathrm{T} \Rightarrow \mathrm{p}=\mathrm{F}$