Translate the following inference to logic notation: For all x, if x were happy, then x is a musician. For all x, x is a musician if and only if x is happy. Therefore for all x, x is happy if and only if x is a musician.
forall x: P(x) -> Q(x). forall x: Q(x) <-> P(x). Therefore forall x: P(x) <-> Q(x).