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Question
The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______
Options
s ∧ ∼r
s ∧ (r ∧ ∼s)
s ∨ (r ∨ ∼s)
s ∧ r
MCQ
Fill in the Blanks
Solution
The negation of ∼s ∨ (∼r ∧ s) is equivalent to s ∧ r.
Explanation:
∼[∼s ∨ (∼r ∧ s)]
≡ s ∧ (r ∨ ∼s) .......[De Morgan's lawl
≡ (s ∧ r) ∨ (s ∧ ∼s) ........... [Distributive Jaw]
≡ (s ∧ r) ∨ F ......... [Complement law]
≡ s ∧ r ......... [Identity law]
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