The Boolean expression (p ∧ ~ q) ⇒ (q ∨ ~ p) is equivalent to:

The Boolean expression

\left(p ∧ ~ q\right) ⇒ \left(q ∨ ~ p\right) is equivalent to:

Options

A $q ⇒ p$
B $p ⇒ q$
C $~ q ⇒ p$
D $p ⇒ ~ q$

Correct answer

B. $p ⇒ q$

Step-by-step solution

We have,

$p$	$q$	$~ p$	$~ q$	$p ∧ ~ q$	$q ∨ ~ p$	$( p ∧ ~ q )$ $⇒ ( q ∨ ~ p )$	$p ⇒ q$
$T$	$F$	$F$	$T$	$T$	$F$	$F$	$F$
$F$	$T$	$T$	$F$	$F$	$T$	$T$	$T$
$T$	$T$	$F$	$F$	$F$	$T$	$T$	$T$
$F$	$F$	$T$	$T$	$F$	$T$	$T$	$T$

$∴ \left(p ∧ ~ q\right) ⇒ \left(q ∨ ~ p\right)$

$≡ p ⇒ q$

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