Translate the following inference to logic notation: For all x, y is not a scientist. There is at least one x for which if y climbs a mountain, then y is a scientist. For all x, y will climb a mountain if and only if y is a scientist. Therefore there is at least one x for which y will not climb a mountain.
forall x: ~P(x). exists x: Q(x) -> P(x). forall x: Q(x) <-> P(x). Therefore exists x: ~Q(x).