Translate the following inference to logic notation: For all x, z is an astronaut if and only if z is an electrician. For all x, z is an astronaut or z is not an electrician. Therefore for all x, if z were an electrician, then z is an astronaut.
forall x: P(x) <-> Q(x). forall x: P(x) or ~Q(x). Therefore forall x: Q(x) -> P(x).