Question

For any two statements p and q, the negation of the expression (p ∧ ∼q) ∧ ∼p is ______ 

Options

• ∼p ∨ ∼q

• p ↔ q

• p ∧ q

• ∼p ∧ ∼q

Answer 1

For any two statements p and q, the negation of the expression (p ∧ ∼q) ∧ ∼p is p ∧ q.

Explanation:

Negation of (p ∧ ∼q) ∨ ∼p is

∼[(p ∧ ∼q) ∨ ∼p]

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

≡ (∼p ∨ q) ∧ p

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

≡ F ∨ (q ∧ p) .................. [Complement law]

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

≡ p ∧ q