Translate the following inference to logic notation: For all x, if x_4 cooks, then x_4 is a bartender. For all x, x_4 will cook if and only if x_4 is a bartender. Therefore for all x, x_4 will cook if and only if x_4 is a bartender.
forall x: P(x) -> Q(x). forall x: P(x) <-> Q(x). Therefore forall x: P(x) <-> Q(x).