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Question
Negation of (p ∧ q) → (∼p ∨ r) is ______.
Options
(p ∨ q) ∧ (p ∧ ∼r)
(p ∧ q) ∨ (p ∧ ∼r)
(p ∧ q) ∧ (p ∧ ∼r)
(p ∨ q) ∨ (p ∧ ∼r)
MCQ
Fill in the Blanks
Solution
Negation of (p ∧ q) → (∼p ∨ r) is (p ∧ q) ∧ (p ∧ ∼r).
Explanation:
Since ∼(p → q) ≡ p ∧ ∼q,
∼[(p ∧ q) → (∼p ∨ r)]
≡ (p ∧ q) ∧ ∼(∼p ∨ r)
≡ (p ∧ q) ∧ (p ∧ ∼r) ......[De Morgan's law]
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Negations of Compound Statements
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