Translate the following inference to logic notation: For all x, x_7 will work if and only if x_7 is a doctor. For all x, x_7 is happy if and only if x_7 will work. Therefore for all x, if x_7 were happy, then x_7 is a doctor.
forall x: P(x) <-> Q(x). forall x: R(x) <-> P(x). Therefore forall x: R(x) -> Q(x).