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Question
Inverse of statement pattern (p ∨ q) → (p ∧ q) is ________ .
Options
(p ∧ q) → (p ∨ q)
∼ (p ∨ q) → (p ∧ q)
(∼p ∧ ∼q) → (∼p ∨ ∼q)
(∼p ∨ ∼q) → (∼p ∧ ∼q)
Solution
Inverse of statement pattern (p ∨ q) → (p ∧ q) is (∼p ∧ ∼q) → (∼p ∨ ∼q).
Explanation:
From De-Morgan’s law: ∼ (p ∨ q) is equivalent to (∼p ∧ ∼q) and ∼ (p ∧ q) is equivalent to (∼p ∨ ∼q).
The inverse of the logic (p ∨ q) → (p ∧ q) is ∼ (p ∨ q) →∼ (p ∧ q) which is equal to (∼p ∧ ∼q) → (∼p ∨ ∼q).
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