Let p and q be two statements. Then ~ ( p ∧ ( p → ~ q ) is...

Given,

$~ ( p ∧ ( p \to ~ q )$

$≡ ~ p ∨ ~ ( ~ p ∨ ~ q )$ \left\{\text{as}A \to B ≡ ~ A ∨ B\right\}$</p><p>$≡ ~ p ∨ ( p ∧ q )$\left\{\text{as} ~ \left(A ∨ B\right) ≡ ~ A ∧ ~ B\right\}$

$≡ ( ~ p ∨ p ) ∧ ( ~ p ∨ q )$

$≡ t ∧ ( ~ p ∨ q )$

$≡ ~ p ∨ q$

$≡ ( ~ p ) ∨ q$