Translate the following inference to logic notation: For all x, y_3 is a musician if and only if y_3 will climb a mountain. For all x, if y_3 were a musician, then y_3 is climbing a mountain. For all x, if y_3 climbs a mountain, then y_3 is a musician. Therefore for all x, y_3 will climb a mountain if and only if y_3 is a musician.
forall x: P(x) <-> Q(x). forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore forall x: Q(x) <-> P(x).