Question

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

• A. True
• B. False
• C. True, if $r$ is false
• D. True, if $q$ is true

Answer 1

The correct option is A True

$\sim p\vee q$ means $F\vee F=F,\sim r$ means $F$

$\therefore \left[\right(\sim p\vee q)\wedge \sim r)=F\wedge F=F$ which imply $p=T$ means $F\Rightarrow T=T$.

Hence, the truth value of the given statement is True.