Translate the following inference to logic notation: For all x, if x_1 cooks, then x_1 is playing squash. For all x, if x_1 sleeps, then x_1 is poor. There is at least one x for which x_1 will sleep or x_1 will cook. For all x, if x_1 were poor, then x_1 is playing squash. Therefore there is at least one x for which x_1 will play squash.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). exists x: R(x) or P(x). forall x: S(x) -> Q(x). Therefore exists x: Q(x).