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