Without using truth table prove that : (p ∨ q) ∧ (p ∨ ~q) ≡ p - Vidyadip

Question

Without using truth table prove that : (p ∨ q) ∧ (p ∨ ~q) ≡ p

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Answer

LHS = (p ∨ q) ∧ (p ∨ ~q)
≡ p ∨ (q ∧ ~q) … (Distributive Law)
≡ p ∨ F … (Complement Law)
≡ p … (Identity Law)
≡ RHS.

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