∼ (p ∨ q) ∨ (∼ p ∧ q) is equivalent to

∼ \left(p ∨ q\right) ∨ \left(∼ p ∧ q\right) is equivalent to

Options

A $p$
B $∼ p$
C $q$
D $∼ q$

Correct answer

B. $∼ p$

Step-by-step solution

$\left(p ∨ q\right)$ ∨ $\left( p ∧ q\right)$ ≡ \left( p ∧ q\right) $∨ \left( p ∧ q\right)$ (By De morgan's Law)
$≡ ∼ p ∧ \left(∼ q ∨ q\right) (By complement laws)<br />$ ≡ p ∧ t $(By Identity Laws)</p><p>$ ≡ p $</p>$

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