The negation of the compound proposition p∨ (.∼ p∨ q.) is

Question

The negation of the compound proposition p∨ (.∼ p∨ q.) is (A) (p ∧ ∼ q)∧ ∼ p (B) (.p∧ ∼ q.)∨ ∼ p (C) (.p∨ ∼ q.)∨ ∼ p (D) None of these

Tardigrade Admin · Accepted Answer

From the De Morgan's Law, ∼ (p ∨ q)=∼ p∧ ∼ q So, the negation of p∨ (.∼ p∨ q.) ∼ [.p∨ (.∼ p∨ q.)]. =∼ p∧ ∼ (.∼ p∨ q.) =∼ p∧ (.p∧ ∼ q.)

Q. The negation of the compound proposition $p \lor (\sim p \lor q)$ is