Question

The negation of the Boolean expression ~s∨(~r∧s) is equivalent to:
1. ~s ∧ ~r
2. r
3. s ∨ r
4. s ∧ r

Answer 1

Correct Answer - Option 4 : s ∧ r

The given Boolean expression is ~s ∨ (~r ∧ s)

≡ (~s ∨ ~r) ∧ (~s ∨ s)

≡ (~s ∨ ~r)           (∵ ~s ∨ s) is tautology)

≡ ~(s ∧ r)

Hence, the negation of the Boolean expression ~s ∨ (~r ∧ s) is equivalent to s ∧ r.