Question

The statement pattern [∼r ∧ (p ∨ q) ∧ (p ∨ q) ∧ (∼p ∧ q)] is equivalent to ______ 

Options

• p ∧ q

• r

• p

• q

Answer 1

The statement pattern [∼r ∧ (p ∨ q) ∧ (p ∨ q) ∧ (∼p ∧ q)] is equivalent to q. 

Explanation:

[∼r ∧ (p ∨ q)] ∧ (p ∨ q) ∧ (∼p ∨ q)]

≡ (p ∨ q) ∧ (∼p ∨ q) ........... [Absorption law]

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

≡ F ∨ q ........ [Complement law]

≡ q ..............[Identity Jaw]