Translate the following inference to logic notation: For all x, y will take a plane if and only if y will write a letter. For all x, if y takes a plane, then y is writing a letter. For all x, if y writes a letter, then y is taking a plane. Therefore for all x, y will write a letter if and only if y will take a plane.
forall x: P(x) <-> Q(x). forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore forall x: Q(x) <-> P(x).