Translate the following inference to logic notation: For all x, if y writes a letter, then y is a nurse. For all x, if y were bored, then y is a musician. There is at least one x for which if y were a musician, then y is writing a letter. Therefore there is at least one x for which if y were bored, then y is a nurse.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). exists x: S(x) -> P(x). Therefore exists x: R(x) -> Q(x).