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