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