Translate the following inference to logic notation: If Richard plays squash, then Sarah is an astronaut. For all x, x_15 is an astronaut if and only if x_15 will sleep. If Sarah sleeps, then Richard is playing squash. Therefore if Richard plays squash, then Sarah is sleeping.
p -> P(a). forall x: P(x) <-> Q(x). Q(a) -> p. Therefore p -> Q(a).