InterviewSolution
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Without using truth table prove that :(p ∧ q) ∨ (~ p ∧ q) ∨ (p ∧ ~q) ≡ p ∨ q |
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Answer» LHS = (p ∧ q) v (~p ∧ q) ∨ (p ∧ ~q) ≡ [(p ∨ ~p) ∧ q] ∨ (p ∧ ~q) … (Distributive Law) ≡ (T ∧ q) ∨ (p ∧ ~q) … (Complement Law) ≡ q ∨ (p ∧ ~q) … (Identity Law) ≡ (q ∨ p) ∧ (q ∨ ~q) … (Distributive Law) ≡ (q ∨ p) ∧ T .. (Complement Law) ≡ q ∨ p … (Identity Law) ≡ p ∨ q … (Commutative Law) ≡ RHS. |
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