Translate the following inference to logic notation: For all x, if x_15 were an astronaut, then x_15 is playing squash. If Michael sleeps, then Sarah is playing squash. Sarah is not an astronaut. For all x, x_15 will play squash if and only if x_15 is an astronaut. Therefore Michael is not sleeping.
forall x: P(x) -> Q(x). p -> Q(a). ~P(a). forall x: Q(x) <-> P(x). Therefore ~p.