Translate the following inference to logic notation: For all x, x_6 is excited if and only if x_6 is a scientist. For all x, x_6 is excited or x_6 is not a scientist. Therefore for all x, x_6 is excited if and only if x_6 is a scientist.
forall x: P(x) <-> Q(x). forall x: P(x) or ~Q(x). Therefore forall x: P(x) <-> Q(x).