Question

The truth values of $p,q$ and$r$ for which $(p\wedge q)\vee (~r)$ has truth value $F$ are respectively

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

Answer 1

The correct option is E

$F,F,T$

Explanation for the correct option:

Form the truth table for the given expression to find the required solution as below:

$p$	$q$	$r$	$\left(~r\right)$	$\left(p\wedge q\right)$	$\left(p\wedge q\right)\vee \left(~r\right)$
$T$	$T$	$T$	$F$	$T$	$T$
$T$	$T$	$F$	$T$	$T$	$T$
$T$	$F$	$T$	$F$	$F$	$F$
$T$	$F$	$F$	$T$	$F$	$T$
$F$	$T$	$T$	$F$	$F$	$F$
$F$	$T$	$F$	$T$	$F$	$T$
$F$	$F$	$T$	$F$	$F$	$F$
$F$	$F$	$F$	$T$	$F$	$T$

Hence, from the truth table we can deduce that the truth value of $\left(p\wedge q\right)\vee \left(~r\right)$ is $F$ for the truth values of $p,q$ and $r$ which are

$\left(T,F,T\right)$, $\left(F,T,T\right)$,or $\left(F,F,T\right)$ respectively.

Among the given options, $\left(F,F,T\right)$ is the only answer that matches with the given options.

Hence, option(E) is the correct answer.