1.

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

Answer»

LHS = (p ∨ q) ∧ (p ∨ ~q) 

≡ p ∨ (q ∧ ~q) … (Distributive Law) 

≡ p ∨ F … (Complement Law) 

≡ p … (Identity Law) 

≡ RHS.



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