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Question
The negation of p → (~p ∨ q) is ______
Options
p ∨ (p ∨ ∼q)
p → ∼(p ∨ q)
p → q
P ∧ ∼q
MCQ
Fill in the Blanks
Solution
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]
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