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)

Answer 1

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).