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Q.

The contra positive of $(∼ p ∧ q) → (q ∧ ∼ r)$ is

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a

r ∧ (p ∧ ∼ q)

b

r ∧ (∼ p ∨ q)

c

∼ r ∨ (p ∨ ∼ q)

d

∼ r ∨ (∼ p ∧ q)

answer is C.

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Detailed Solution

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Contra positive of the given statements is
$~ (q \land ~ r) \to ~ (~ p \land q) \equiv (~ q \lor r) \to (p \lor ~ q)$
$≡ ∼ (− q ∨ r) ∨ (p ∨ − q) ≡ (q ∧ − r) ∨ (p ∨ ∼ q)$
$≡ [q ∨ (p ∨ ∼ q)] ∧ [∼ r ∨ (p ∨ ∼ q)] ≡ [p ∨ (q ∨ ∼ q)] ∧ [∼ r ∨ (p ∨ ∼ p)]$
$≡ (P ∨ T) ∧ (∼ r ∨ (p ∨ ∼ q)) ≡ T ∧ (∼ r ∨ (p ∨ ∼ q)) = − r ∨ (p ∨ ∼ q)$

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