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

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Without using truth table prove that :

(p ∨ q) ∧ (p ∨ ~q) ≡ p

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1 Answer

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LHS = (p ∨ q) ∧ (p ∨ ~q) 

≡ p ∨ (q ∧ ~q) … (Distributive Law) 

≡ p ∨ F … (Complement Law) 

≡ p … (Identity Law) 

≡ RHS.

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