Translate the following inference to logic notation: Karen is not fast. For all x, x_7 is a mechanic if and only if x_7 is an astronaut. If Charles were a mechanic, then Karen is a poet. For all x, x_14 is fast if and only if x_14 is a poet. Therefore Charles is not an astronaut.
~P(a). forall x: Q(x) <-> R(x). Q(b) -> S(a). forall x: P(x) <-> S(x). Therefore ~R(b).