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! Hehehhe….

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