Question

The negation of $p\wedge q\to p\vee qis$

• A. (p ∧ q ) ∨ (∼ p ∧ ∼ q)
• B. (p ∧ q) ∧ (∼ p ∧ ∼q)
• C. (p ∧ q ) ∨ (∼ p ∨ ∼q)
• D. (p ∧ q) ∧ (∼ p ∨ ∼ q)

Answer 1

The correct option is B

(p ∧ q) ∧ (∼ p ∧ ∼q)

$\sim \left[\right(p{\wedge }^0†)\to (p{\vee }^0†\left)\right]\equiv (p{\wedge }^0†)\wedge \sim (p{\vee }^0†)\equiv (p{\wedge }^0†)\wedge (\sim p\wedge {\sim }^0†)$