Translate the following inference to logic notation: There is at least one x for which if x takes a plane, then x is writing a letter. For all x, x will write a letter if and only if x will take a plane. Therefore there is at least one x for which if x takes a plane, then x is writing a letter.
exists x: P(x) -> Q(x). forall x: Q(x) <-> P(x). Therefore exists x: P(x) -> Q(x).