Contoh Soal

Buktikan [(p → q) ˄p] → q ek T

Bukti :

Jelas :    [( p →  q ) ˄ p ] → q

                ≡ [( ~p  v  q) ˄ p ] → q                       (hk. implikasi)

                ≡~ [( ~p  v  q ) ˄ p ] v q                      (hk. implikasi)

                ≡ [~(~p  v  q ) v ~p ] v q                     (hk. DM)

                ≡ [(~(~p)  ^  ~q ) v ~p ] v q                (hk. DM)

                ≡ [(p  ^  ~q ) v ~p ] v q                       (hk. Komplemen)

                ≡ [(p  v  ~p ) ^(~q v  ~p) ] v q            (hk. Distributis )

                ≡ [T ^(~q v  ~p) ] v q                          (hk. Komplemen)

                ≡ (~q v  ~p)  v q                                  (hk. Identitas)

                ≡ ~q v ( ~p  v q)                                  (hk. Asosiatif)

                ≡ ~q v ( q  v ~p)                                  (hk. Komutatif)

                ≡(~q v q) v  ~p                                    (hk.Asosiatif)

                ≡ T v ~p                                               (hk. Komplemen)

                ≡ T                                                       (hk. Identitas)

Jadi [(p → q) ˄p] → q ek T BENAR! yeeeeeeeeeeeee
by Kelompok 6

File : Pembuktian Contoh Soal ( kel 6 )