Question

If truth value for $p\to (q\vee r)$ is false, then the truth values of $p,q,r$ are respectively :

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

Answer 1

The correct option is A $T,F,F$

We know that $s\to t$ is false, iff $s$ is true and $t$ is false.
So, $p\to (q\vee r)$ will be false, iff $p$ is true and $q\vee r$ is false.
$q\vee r$ is false only when both $q$ and $r$ are false.
$\therefore$ Truth values for $(p,q,r)\equiv (T,F,F)$