If$(\mathrm{p}\wedge ~\mathrm{q})\wedge (\mathrm{p}\wedge \mathrm{r})\to \sim \mathrm{p}\vee \mathrm{q}$ is false then the truth values of p,q and r are respectively

$(\mathrm{p}\wedge ~\mathrm{q})\wedge (\mathrm{p}\wedge \mathrm{r})\to \sim \mathrm{p}\vee \mathrm{q}$  is false if

$(\mathrm{p}\wedge ~\mathrm{q})\wedge (\mathrm{p}\wedge \mathrm{r})$ is true and $~\mathrm{p}\vee \mathrm{q}$is false

$(\mathrm{p}\wedge ~\mathrm{q})\wedge (\mathrm{p}\wedge \mathrm{r})$ is true if both $\mathrm{p}\wedge ~\mathrm{q}$ and $\mathrm{p}\wedge \mathrm{r}$ are true

$\therefore$ $$\begin{gathered} \mathrm{p} \mathrm{and} ~\mathrm{q} \mathrm{are} \mathrm{true} \\ \Rightarrow \mathrm{p} \mathrm{is} \mathrm{true} \mathrm{and} \mathrm{q} \mathrm{is} \mathrm{false} \end{gathered}$$

$\mathrm{p}\wedge \mathrm{r}$ is true if both p and r are true statements

Therefore truth values of p,q,r are T,F,T