Question

The Boolean expression : $~(p\vee q)\vee (~p\wedge q)$ is equivalent to:

• A. $q$
• B. $~q$
• C. $~p$
• D. $p$

Answer 1

The correct option is C

$~p$

Explanation for the correct answer:

Form the truth table to evaluate the truth value of the required expression

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

From the truth table we have formed for the given expression,

We can observe that the truth values for the given expression $~(p\vee q)\vee (~p\wedge q)$ and $~p$ are identical.

Hence, we can conclude that the given Boolean expression $~(p\vee q)\vee (~p\wedge q)$ is equivalent to $~p$

$\Rightarrow$$~(p\vee q)\vee (~p\wedge q)\equiv ~p$

Hence, option $\left(C\right)$ is the correct answer.