Give a proof of the following equivalence following the patt

Give a proof of the following equivalence following the pattern of proof shown in the examples on pages 38 and 39 of the text: ¬p (p q) T.

Solution

Consider

¬p (p q) ¬p (¬p V q)     since p q ¬p V q

                        ¬( ¬p) V (¬p V q)   

                        ¬( ¬p ) V (¬p V q) use law of double negation ¬( ¬p ) p

                          p V ( ¬p V q ) use associative law

                         ( p V ¬p ) V q     since p V ¬p T

                       T V q            since T V q T

                       T

Thus , ¬p (p q) T.