Translate the following inference to logic notation: For all x, if x_3 were a sailor, then x_3 is a cashier. For all x, x_3 is a doctor or x_3 is not a cashier. There is at least one x for which x_3 is a musician if and only if x_3 is a doctor. For all x, x_3 is a sailor or x_3 is a musician. Therefore there is at least one x for which x_3 is a doctor.
forall x: P(x) -> Q(x). forall x: R(x) or ~Q(x). exists x: S(x) <-> R(x). forall x: P(x) or S(x). Therefore exists x: R(x).