Translate the following inference to logic notation: For all x, x_10 is a bartender if and only if x is a mechanic. For all x, if x_10 were a nurse, then x is a mechanic. For all x, x_10 is a bartender. Therefore there is at least one x for which x is a mechanic.
forall x: P(x) <-> Q(x). forall x: R(x) -> Q(x). forall x: P(x). Therefore exists x: Q(x).