Translate the following inference to logic notation: For all x, x_10 will sleep and x_10 is sad. There is at least one x for which if x_10 were a writer, then x_10 is sleeping. For all x, if x_10 sleeps, then x_10 is a writer. Therefore there is at least one x for which x_10 is a writer.
forall x: P(x) and Q(x). exists x: R(x) -> P(x). forall x: P(x) -> R(x). Therefore exists x: R(x).