Question

The Boolean expression $\left(\sim \left(p\wedge q\right)\right)\vee q$ is equivalent to :

• A. $q\to \left(p\wedge q\right)$
• B. $p\to q$
• C. $p\to (p\to q)$
• D. $p\to (p\vee q)$

Answer 1

Answer: (D)

$\left(\sim \left(p^{\wedge }q\right)\right)\vee q$
$=(\sim p\vee \sim q)\vee q$
$=\sim p\vee \sim q\vee q$
$=\sim p\vee t$
$=$ this statement is a tautology option $D$
$p\Rightarrow (p\vee q)$ is also a tautology.
$OR$

$p$	$q$	$p\wedge q$	$\sim (p\wedge q)$	$\sim \left(p^{\wedge }q\right)\vee q$	$p\vee q$	$p\to (p\vee q)$
T	T	T	F	T	T	T
T	F	F	T	T	T	T
F	T	F	T	T	T	T
F	F	F	T	T	F	T