Question

The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ______ 

Options

• p

• q

• ∼q

• ∼p

Answer 1

The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ∼p.

Explanation:

∼(p ∨ q) ∨ (∼p ∧ q)

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

≡ ∼p ∧ (∼q ∨ q) .............. (Distributive law]

≡ ∼p ∧ T ................. [Complement law]

≡ ∼p .................... [Identity law]