Translate the following inference to logic notation: For all x, y is a writer if and only if y is a scientist. There is at least one x for which if y were a scientist, then y is a writer. For all x, y is not a scientist. Therefore there is at least one x for which y is not a writer.
forall x: P(x) <-> Q(x). exists x: Q(x) -> P(x). forall x: ~Q(x). Therefore exists x: ~P(x).