Question

Let $p,q,r$ be three statements such that the truth value of $(p\wedge q)\to (~q\vee r)$ is $F.$ Then the truth values of$p,q,r$ are respectively:

• A. F, T, F
• B. T, F, T
• C. T, T, F
• D. T, T, T

Answer 1

The correct option is C

T, T, F

Explanation for the correct option:

Finding the truth value of $p,q,r$

$(p\wedge q)\to (~q\vee r)=\text{F}$
when $(p\wedge q)=T$
and $(~q\vee r)=F$
So $(p\wedge q)=T$ is possible when $p=q=T$
$\therefore ~q=F$
So $(~q\vee r)=\text{F}$ is possible if $r$ is false
$\therefore p=T,q=T,r=F$

Hence the correct option is (C).