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