Question
The Boolean Expression (p∧~q)∨q∨(~p∧q) is equivalent to:
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~p ∧ q
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p ∧ q
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p ∨ q
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p ∨ ~ q
Solution
C.
p ∨ q
Consider, (p ∧~q) ∨ q ∨(~p ∧ q)
≡ [(p ∧~q) ∨ q] ∨ (~p ∧ q)
≡[(p ∨~q) ∧ t] ∨ (~p ∧ q)
≡((p ∨ q) ∨ (~p ∧ q)
≡(p ∨ q ∨ ~p) ∧ (p ∨ q ∨ q)
≡(q ∨ t) ∧ (p ∨ q)
≡ t ∧ (p ∨ q)
≡ p ∨ q
