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If $(\mathrm{p} \wedge \sim \mathrm{q}) \wedge(\mathrm{p} \wedge \mathrm{r}) \rightarrow \sim p \vee q$ is false, then the truth values of $\mathrm{p}, \mathrm{q}$ and $\mathrm{r}$ are respectively
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$\mathrm{T}, \mathrm{F}, \mathrm{T}$
$\mathrm{T}, \mathrm{F}, \mathrm{T}$
As the truth table for the $(p \wedge \sim q) \wedge(p \wedge r)$ $\rightarrow \sim p \vee q$ is false, then only possible values of $(p, q, r)$ is $(T, F, T)$
$\begin{array}{llllll}p & q & r & \sim q & p \wedge \sim q & p \wedge r \\ \sim p & \sim p \vee q & (p \wedge \sim q) \wedge(p \wedge r)(p \wedge \sim q) \wedge(p \wedge r) \\ \rightarrow \sim p \vee q\end{array}$
$\begin{array}{llllll}p & q & r & \sim q & p \wedge \sim q & p \wedge r \\ \sim p & \sim p \vee q & (p \wedge \sim q) \wedge(p \wedge r)(p \wedge \sim q) \wedge(p \wedge r) \\ \rightarrow \sim p \vee q\end{array}$
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