Translate the following inference to logic notation: For all x, if x_1 sleeps, then x_1 is a bartender. For all x, x_1 will sleep. For all x, x_1 will take a plane if and only if x_1 is a bartender. Therefore for all x, x_1 is a bartender.
forall x: P(x) -> Q(x). forall x: P(x). forall x: R(x) <-> Q(x). Therefore forall x: Q(x).