Translate the following inference to logic notation: There is at least one x for which if x_1 were a mechanic, then x_1 is taking a plane. For all x, if x_1 takes a plane, then x_1 is a mechanic. Therefore there is at least one x for which if x_1 takes a plane, then x_1 is a mechanic.
exists x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore exists x: Q(x) -> P(x).