Translate the following inference to logic notation: For all x, x_15 is a writer. For all x, if x_15 were a writer, then x_15 is an astronaut. There is at least one x for which x_15 is an astronaut if and only if x_15 is rich. Therefore there is at least one x for which x_15 is rich or x_15 is happy.
forall x: P(x). forall x: P(x) -> Q(x). exists x: Q(x) <-> R(x). Therefore exists x: R(x) or S(x).