Question

The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______

विकल्प

• s ∧ ∼r

• s ∧ (r ∧ ∼s)

• s ∨ (r ∨ ∼s)

• s ∧ r

Answer 1

The negation of ∼s ∨ (∼r ∧ s) is equivalent to s ∧ r.

Explanation:

∼[∼s ∨ (∼r ∧ s)] 

≡ s ∧ (r ∨ ∼s)  .......[De Morgan's lawl

≡ (s ∧ r) ∨ (s ∧ ∼s) ........... [Distributive Jaw]

≡ (s ∧ r) ∨ F  ......... [Complement law]

≡ s ∧ r ......... [Identity law]