Question

Negation of (p ∧ q) → (∼p ∨ r) is ______.

विकल्प

•  (p ∨ q) ∧ (p ∧ ∼r)

•  (p ∧ q) ∨ (p ∧ ∼r)

•  (p ∧ q) ∧ (p ∧ ∼r)

•  (p ∨ q) ∨ (p ∧ ∼r)

Answer 1

Negation of (p ∧ q) → (∼p ∨ r) is (p ∧ q) ∧ (p ∧ ∼r).

Explanation:

Since ∼(p → q) ≡ p ∧ ∼q,

∼[(p ∧ q) → (∼p ∨ r)]

≡ (p ∧ q) ∧ ∼(∼p ∨ r)

≡ (p ∧ q) ∧ (p ∧ ∼r)  ......[De Morgan's law]