Translate the following inference to logic notation: There is at least one x for which x is happy if and only if x is a musician. For all x, if x works, then x is happy. For all x, if x were a musician, then x is working. Therefore there is at least one x for which x is a musician if and only if x is happy.
exists x: P(x) <-> Q(x). forall x: R(x) -> P(x). forall x: Q(x) -> R(x). Therefore exists x: Q(x) <-> P(x).