Translate the following inference to logic notation: For all x, x_4 will go running or x_4 will cook. There is at least one x for which if x_4 cooks, then x_4 is drinking water. For all x, x_4 will drink water if and only if x_4 will go running. Therefore there is at least one x for which x_4 will drink water.
forall x: P(x) or Q(x). exists x: Q(x) -> R(x). forall x: R(x) <-> P(x). Therefore exists x: R(x).