Translate the following inference to logic notation: For all x, if y were a lawyer, then y is sleeping. There is at least one x for which y will sleep if and only if y is a lawyer. Therefore there is at least one x for which if y were a lawyer, then y is sleeping.
forall x: P(x) -> Q(x). exists x: Q(x) <-> P(x). Therefore exists x: P(x) -> Q(x).