Propositional form X is inconsistent with propositional form Y (i.e., X and Y are inconsistent [with one another]) iff it is impossible for both X and Y to be true.
Example from everyday life: 'x is six feet tall' is inconsistent with 'x is less than six feet tall'
Example from categorical logic: 'All S are P' is inconsistent with 'No S are P' (iff at least one S exists)
Example from propositional logic: 'p • q' is inconsistent with '~p ∨~q'
Example from predicate logic: '(x)~Øx' is inconsistent with '(Ǝx)Øx'
