Question

Let $p,q,r$ be three statements such that the truth value of $(p\wedge q)\to (\sim q\vee r)$ 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 $T,T,F$

$(p\wedge q)\to (\sim q\vee r)$ is $F$ only when
$p\wedge q$ is $T$ and $\sim q\vee r$ is $F.$

$\Rightarrow p\wedge q$ is $T$ when $p$ is $T$ and $q$ is $T.$
$\Rightarrow \sim q\vee r$ is $F$ as $\sim q$ is $F,$ then $r$ is $F.$

$\therefore p,q,r\equiv T,T,F$