Translate the following inference to logic notation: There is at least one x for which if x_7 were happy, then x_7 is not cooking. For all x, x_7 is a bartender. For all x, x_7 is a bartender if and only if x_7 will cook. Therefore there is at least one x for which x_7 is not happy.
exists x: P(x) -> ~Q(x). forall x: R(x). forall x: R(x) <-> Q(x). Therefore exists x: ~P(x).