Translate the following inference to logic notation: For all x, x_5 is a scientist. For all x, x_5 will work if and only if x_5 is a poet. For all x, if x_5 were a scientist, then x_5 is working. Therefore for all x, x_5 will work.
forall x: P(x). forall x: Q(x) <-> R(x). forall x: P(x) -> Q(x). Therefore forall x: Q(x).