Translate the following inference to logic notation: For all x, if x were a doctor, then x is playing squash. There is at least one x for which x will play a game or x will not sleep. For all x, x will play squash if and only if x will sleep. Therefore there is at least one x for which if x were a doctor, then x is playing a game.
forall x: P(x) -> Q(x). exists x: R(x) or ~S(x). forall x: Q(x) <-> S(x). Therefore exists x: P(x) -> R(x).