Translate the following inference to logic notation: For all x, z is a mechanic. There is at least one x for which z is happy if and only if z is a mechanic. For all x, z is not happy. Therefore there is at least one x for which z is a soldier.
forall x: P(x). exists x: Q(x) <-> P(x). forall x: ~Q(x). Therefore exists x: R(x).