0 votes 0 votes Determine whether (p ∧ ( p → q )) → q is Tautology , Contradiction or Contingency. Mathematical Logic discrete logic + – LavTheRawkstar asked Jun 26, 2016 edited Jul 28, 2016 by Prashant. LavTheRawkstar 447 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 3 votes 3 votes p q p → q p ∧ ( p → q ) (p ∧ ( p → q )) → q 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 Since , all are 1, hence tautology Kapil answered Jun 26, 2016 selected Jun 26, 2016 by LavTheRawkstar Kapil comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes (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. LeenSharma answered Jul 28, 2016 LeenSharma comment Share Follow See 1 comment See all 1 1 comment reply Tauhin Gangwar commented Jul 28, 2016 reply Follow Share good one ...accurate procedure ..it tells u know the concept well 2 votes 2 votes Please log in or register to add a comment.