Sum
Without using truth table prove that:
(p ∨ q) ∧ (p ∨ ∼ q) ≡ p
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Solution
L.H.S. = (p ∨ q) ∧ (p ∨ ∼ q)
≡ p ∨ (q ∧ ∼ q) ..........(Distributive Law)
≡ p ∨ F .........(Complement Law)
≡ p .........(Identity Law)
= R.H.S.
Concept: Algebra of Statements
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