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,$p\to (q\vee r)\Rightarrow \sim p\vee (q\vee r)$
Now putting values
$T,F,F\Rightarrow \sim T\vee (F\vee F)=F$
$F,F,F\Rightarrow \sim F\vee (F\vee F)=T$
$F,F,T\Rightarrow \sim F\vee (F\vee T)=T$
$T,T,F\Rightarrow \sim T\vee (T\vee F)=T$
Hence, $T,F,F$ is correct.

$\text{Alternate Solution}$
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
$\therefore$ Truth values for $(p,q,r)\equiv (T,F,F)$