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