## Discrete Mathematics with Applications 4th Edition

Recall the definition of only if: "$\forall x$, r(x) only if s(x)" means "$\forall x$, if ~s(x) then ~r(x)" or equivalently "$\forall x$, if r(x) then s(x). Recall also the definition of inverse of a statement: A statement of the form: $\forall x \in D$, if P(x) then Q(x), and as its inverse statement: $\forall x \in D$, if ~P(x) then ~Q(x)." The inverse is not logically equivalent to the original statement.