Translate the following inference to logic notation: For all x, if x_1 were an astronaut, then x_1 is an artist. For all x, if x_1 were an artist, then x_1 is an astronaut. Patricia is an artist if and only if Robert is an electrician. For all x, x_1 is not an astronaut. Therefore Robert is not an electrician.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). Q(a) <-> p. forall x: ~P(x). Therefore ~p.