Propositional form X is independent of propositional form Y (i.e., X and Y are independent [of one another]) iff (1) it is possible for X to be true while Y is false; (2) it is possible for Y to be true while X is false; (3) it is possible for both X and Y to be true; and (4) it is possible for both X and Y to be false.
Example from everyday life: ‘x is five feet 10 inches tall’ is independent of ‘x weighs 155 pounds’
Example from categorical logic: ‘All S are P’ is independent of ‘All P are S’ (this is conversion of an ‘A’ proposition)
Example from propositional logic: ‘p’ is independent of ‘p ≡ q’
Example from predicate logic: ‘(x)~Øx’ is independent of ‘(Ǝx)~Øx’
