Translate the following inference to logic notation: For all x, if y were sad, then y is a musician. There is at least one x for which if y were a musician, then y is climbing a mountain. For all x, if y climbs a mountain, then y is sad. Therefore there is at least one x for which y is a musician if and only if y will climb a mountain.
forall x: P(x) -> Q(x). exists x: Q(x) -> R(x). forall x: R(x) -> P(x). Therefore exists x: Q(x) <-> R(x).