Translate the following inference to logic notation: For all x, if z were a janitor, then z is climbing a mountain. For all x, if z climbs a mountain, then z is a janitor. There is at least one x for which if z were a cashier, then z is a janitor. For all x, if z were a janitor, then z is a cashier. Therefore there is at least one x for which if z climbs a mountain, then z is a cashier.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). exists x: R(x) -> P(x). forall x: P(x) -> R(x). Therefore exists x: Q(x) -> R(x).