Translate the following inference to logic notation: For all x, z_1 is happy if and only if z_1 will drink water. There is at least one x for which if z_1 were happy, then z_1 is drinking water. Therefore there is at least one x for which if z_1 were happy, then z_1 is drinking water.
forall x: P(x) <-> Q(x). exists x: P(x) -> Q(x). Therefore exists x: P(x) -> Q(x).