Show that
(i) ` ~ [ p ^^ ( ~p) ]` is a tautology
(ii) ` ~ [ p vee ( ~ p)]` is a contradication.

Explanation

(i) The truth table of ` ~[ p ^^ ( ~p) ]` is given by

Since th truth table of ` ~ [ p ^^ ( ~ p)]` contains only T in the last column.
So ` ~[ p ^^ ( ~p) ]` is a tautology.
(ii) The truth table of `~ [ p vee (~p) ]`

Since the truth table contains only F in the last column.
Hence, ` ~ [ p vee (~p)]` is a contradiction.