Question

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

• A. T, F and F
• B. F, F and T
• C. F, T and T
• D. T, F and T

Answer 1

The correct option is A

T, F and F

Explanation for Correct option

Since $(\mathrm{p}\wedge ~\mathrm{r})\to (~\mathrm{p}\vee \mathrm{q})\equiv F$

$\Rightarrow (\mathrm{p}\wedge ~\mathrm{r})\equiv \mathrm{T}\&(~\mathrm{p}\vee \mathrm{q})\equiv \mathrm{F}$

$\Rightarrow \mathrm{P}\equiv \mathrm{T},~r\equiv \mathrm{T}\mathrm{and}~\mathrm{p}\equiv \mathrm{F},\mathrm{q}\equiv \mathrm{F}$

$\Rightarrow \mathrm{p}\equiv \mathrm{T},\mathrm{q}\equiv \mathrm{F},\mathrm{r}\equiv \mathrm{F}$

$\therefore$ $p$ is true, $r$ is false and $q$ is false.

Hence Option (A) is correct.