Translate the following inference to logic notation: For all x, if x writes a letter, then x is sleeping. There is at least one x for which if x sleeps, then x is writing a letter. For all x, x will sleep. Therefore there is at least one x for which x will write a letter.
forall x: P(x) -> Q(x). exists x: Q(x) -> P(x). forall x: Q(x). Therefore exists x: P(x).