Question

The negation of p → (~p ∨ q) is ______ 

पर्याय

• p ∨ (p ∨ ∼q)

• p → ∼(p ∨ q) 

• p → q

• P ∧ ∼q

Answer 1

The negation of p → (~p ∨ q) is P ∧ ∼q.

Explanation:

~[p → (~p ∨ q)]

≡ p ∧ ~(~p ∨ q).........[∵  ~(p → q) ≡ p ∧ ~q]

≡ p ∧ (p ∧ ~q) .....[De Morgan's law)

≡ p ∧ ~q ..........[Absorption Jaw]