Question

The negation of the Boolean expression (r ∧ ∼s) ∨ s is equivalent to: ______ 

Options

• ∼r ∧ ∼s

• r

• s ∧ r

• s ∨ r

Answer 1

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

Explanation:

Negation of (r ∧ ∼s) ∨ s is

∼[(r ∧ ∼s) ∨ s]

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

≡ (∼r ∨ s) ∧ ∼s 

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

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

≡ (∼r ∧ ∼s) ....[Identity law]