Translate the following inference to logic notation: For all x, x_8 will climb a mountain. There is at least one x for which x_8 is a musician. For all x, x_8 is a bartender if and only if x_8 will climb a mountain. Therefore there is at least one x for which x_8 is a musician and x_8 is a bartender.
forall x: P(x). exists x: Q(x). forall x: R(x) <-> P(x). Therefore exists x: Q(x) and R(x).