Translate the following inference to logic notation: There is at least one x for which if y were sad, then y is a politician. For all x, if y were a politician, then y is sleeping. For all x, if y sleeps, then y is sad. Therefore there is at least one x for which if y were a politician, then y is sleeping.
exists x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: R(x) -> P(x). Therefore exists x: Q(x) -> R(x).