Question

Without using truth table, show that

~ [(p ∧ q) → ~ q] ≡ p ∧ q

Answer 1

L.H.S.

≡ ~ [(p ∧ q) → ~ q]

≡ (p ∧ q) ∧ ~ (~ q)   ....[Negation of implication]

≡ (p ∧ q) ∧ q      .....[Negation of a negation]

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

≡ p ∧ q          .....[Idempotent law]

≡ R.H.S.