Translate the following inference to logic notation: For all x, z is a carpenter and z will play tennis. There is at least one x for which z is a cashier. For all x, if z were a cashier, then z is a musician. Therefore there is at least one x for which z is a musician and z is a carpenter.
forall x: P(x) and Q(x). exists x: R(x). forall x: R(x) -> S(x). Therefore exists x: S(x) and P(x).