Question

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

Options

• p

• ∼r

• ∼p

• ∼q

Answer 1

The logical statement [∼(q ∨ ∼r) ∨ (p ∧ r)] ∧ (q ∨ p) is equivalent to: p 

Explanation:

[∼(q ∨ ∼r) ∨ (p ∧ r)] ∧ (q ∨ p)

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

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

≡ r ∧ [(p ∨∼q) ∧ (p ∨ q)] ........... [Commutative and Associative law]

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

≡ p ∧ [p ∨ F] ............... [Complement law]

≡ p ∧ p ..................... [Identity law]

≡ p