Question

(p ∧∼ q) ∧ (∼ p ∧ q) is ______.

Options

• A tautology

• A contradiction

• Both a tautology and a contradiction

• Neither a tautology nor a contradiction

Answer 1

(p ∧∼ q) ∧ (∼ p ∧ q) is a contradiction.

Explanation:

(p ∧∼ q) ∧ (∼ p ∧ q) = (p ∧∼ q) ∧ (∼ q ∧ q)

= f ∧ f = f

(By using associative laws and commutative laws)

∴ (p ∧∼ q) ∧ (∼ p ∧ q) is a contradiction.