Inverse (logic)

In logic, the inverse is a statement formed by reversing the expression. In traditional logic, the inverse can take two possible forms. The inverse of a statement "All P are Q" could be "All not P are Q" or "All not P are not Q". The first of these is the disjunction of statements P and Q, traditionally written P v Q. The second of these is the converse (logic) of the contrapositive, or the contrapositive of the converse, of the original statement "All P are Q." The denial of a statement does not imply the truth of the inverse. To see this, note that it is not the case that "all women are Virginia Woolf" (cf. bell hooks) but it is also not the case that the first inverse of the statement, "all non-women are Virginia Woolf," holds (cf. Winston Churchill). (Compare this with the contrapositive, "If something is not a woman, then it is not Virginia Woolf.")