Propositional form X is the contradictory of propositional form Y (i.e., X and Y are contradictories [of one another]) iff (1) it is impossible for both X and Y to be true and (2) it is impossible for both X and Y to be false.
Example from everyday life: 'Virtue can be taught' is the contradictory of 'Virtue cannot be taught'
Example from categorical logic: 'No S are P' is the contradictory of 'Some S are P'
Example from propositional logic: 'p • q' is the contradictory of 'p ﬤ ~q'
Example from predicate logic: '(x)~Øx' is the contradictory of '(Ǝx)Øx'
