The Boolean expression ∼ (p ⇒ (∼ q)) is equivalent to

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(∼ p) ⇒ q

p ∨ q

q ⇒ ∼ p

p ∧ q

answer is D.

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Detailed Solution

Here, The given Boolean expression is ∼ (p ⇒ (∼ q)) .
p ⇒ (∼ q) is interpreted as (∼ p∨ ∼ q)
Now, ∼ (p ⇒ (∼ q)) can be written as ∼ (∼ p∨ ∼ q)
∼ (∼ p∨ ∼ q) can be interpreted as ∼ (∼ p) ∧ ∼ (∼ q)
By applying double complement law we can write
∼ (∼ p) ∧ ∼ (∼ q) is equivalent to p ∧ q
Thus, the given Boolean expression ∼ (p ⇒ (∼ q)) is equivalent to p ∧ q .

Hence, option (4) is correct for this question.

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