Determine whether (p ∧ ( p → q )) → q is Tautology , Contradiction or Contingency.
Since , all are 1, hence tautology
(p ∧ ( p → q )) → q
≡(p ∧ ( ~ p ∨ q )) → q
≡~(p ∧ ( ~ p ∨ q )) ∨ q
≡(~p ∨ ( p ∧ ~q )) ∨ q
≡(~p ∨ p ) ∧ ( ~p ∨ ~q ) ∨ q
≡( ~p ∨ ~q ) ∨ q
≡~p ∨ (~q ∨ q)
≡~p ∨ T
≡T
Hence,(p ∧ ( p → q )) → q is Tautology.
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