Without using truth table, show that p ∧ [(~ p ∨ q) ∨ ~ q] ≡ p - Mathematics and Statistics

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Sum

Without using truth table, show that

p ∧ [(~ p ∨ q) ∨ ~ q] ≡ p

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Solution

L.H.S.

≡ p ∧ [(~ p ∨ q) ∨ ~ q]

≡ p ∧ [(~ p ∨ (q ∨ ~ q)]     .....[Associative law]

≡ p ∧ (~ p ∨ T)       .....[Complement law]

≡ p ∧ T                 .....[Identity law]

≡ p                       .....[Identity law] 

≡ R.H.S.

  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Exercise 1.9 [Page 22]

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