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If the truth value of the statement

Question:

If the truth value of the statement $\mathrm{P} \rightarrow(\sim \mathrm{p} \vee \mathrm{r})$ is false $(\mathrm{F})$, then the truth values of the statements $\mathrm{p}, \mathrm{q}, \mathrm{r}$ are respectively :

  1. $\mathrm{F}, \mathrm{T}, \mathrm{T}$

  2. T, F, F

  3. T, T, F

  4. T, F, T


Correct Option: , 3

Solution:

$\mathrm{P} \rightarrow(\sim \mathrm{q} \vee \mathrm{r})$

$\sim \mathrm{p} \vee(\sim \mathrm{q} \vee \mathrm{r})$

$\left.\left.\begin{array}{l}\sim \mathrm{p} \rightarrow \mathrm{F} \\ \sim \mathrm{q} \rightarrow \mathrm{F} \\ \mathrm{r} \rightarrow \mathrm{F}\end{array}\right\} \Rightarrow \begin{array}{l}\mathrm{p} \rightarrow \mathrm{T} \\ \mathrm{q} \rightarrow \mathrm{T} \\ \mathrm{r} \rightarrow \mathrm{F}\end{array}\right\}$

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