If the truth value of the statement [(P ( R)) (( R) Q)] is F, then the truth value of whic…

Question

If the truth value of the statement $$(P \wedge(\sim R)) \rightarrow((\sim R) \wedge Q)$$ is F, then the truth value of which of the following is $$\mathrm{F}$$ ?

Accepted Answer

$\mathrm{X} \Rightarrow \mathrm{Y}$ is a false

when $X$ is true and $Y$ is false

So, $\mathrm{P} \rightarrow \mathrm{T}, \mathrm{Q} \rightarrow \mathrm{F}, \mathrm{R} \rightarrow \mathrm{F}$

(A) $\mathrm{P} \vee \mathrm{Q} \rightarrow \sim \mathrm{R}$ is $\mathrm{T}$

(B) $\mathrm{R} \vee \mathrm{Q} \rightarrow \sim \mathrm{P}$ is $\mathrm{T}$

(C) $\sim(\mathrm{P} \vee \mathrm{Q}) \rightarrow \sim \mathrm{R}$ is $\mathrm{T}$

(D) $\sim(\mathrm{R} \vee \mathrm{Q}) \rightarrow \sim \mathrm{P}$ is $\mathrm{F}$

Solutions · 1