Question

If$p,q,r$ are simple propositions with truth values $T,F,T$then the truth value of $\left[\right(~p\vee q)\wedge ~r]\Rightarrow p$ is

• A. True
• B. False
• C. True, if r is false
• D. None of these

Answer 1

The correct option is A

True

Explanation for the correct option

$p,q,r$ are simple propositions with truth values $T,F,T$

$$\begin{gathered} \Rightarrow ~\mathrm{p}\vee \mathrm{q}\mathrm{means}\mathrm{F}\vee \mathrm{F}=\mathrm{F} \\ \Rightarrow ~\mathrm{r}\mathrm{means}\mathrm{F} \\ \therefore \left[\right(~\mathrm{p}\vee \mathrm{q})\wedge ~\mathrm{r})=\mathrm{F}\wedge \mathrm{F}=\mathrm{F} \\ \mathrm{Where}\mathrm{p}=\mathrm{T}\mathrm{means}\mathrm{F}\Rightarrow \mathrm{T}=\mathrm{T}. \end{gathered}$$

The true value of the given statement is True

Hence option ‘a’ is correct.