Translate the following inference to logic notation: For all x, if y writes a letter, then y is working. For all x, y is a carpenter or y is a poet. For all x, if y were a poet, then y is writing a letter. There is at least one x for which y will work if and only if y is a carpenter. Therefore there is at least one x for which y will work.
forall x: P(x) -> Q(x). forall x: R(x) or S(x). forall x: S(x) -> P(x). exists x: Q(x) <-> R(x). Therefore exists x: Q(x).