Question

State the following statement is True or False

If $p,q,r$ are statements, with truth values T, F, T respectively, then the truth value of $(\sim p\vee q)\wedge \sim r\Rightarrow p$ is T

• A. True
• B. False

Answer 1

The correct option is A True

$p,q,r$ are statements with truth values $T,F,T$ respectively

Consider
$(\sim p\vee q)\wedge \sim r\Rightarrow p$

$=(F\vee F)\wedge F\Rightarrow T$
$=(F\wedge F)\Rightarrow T$

$=F\Rightarrow T=\sim \left(F\right)\vee T=T\vee T=T$
Clearly, option A.