Translate the following inference to logic notation: For all x, x_8 is a doctor if and only if x_8 will climb a mountain. For all x, x_8 is an office clerk or x_8 will climb a mountain. For all x, if x_8 were an office clerk, then x_8 is a doctor. There is at least one x for which x_8 is rich. Therefore there is at least one x for which x_8 is rich and x_8 is a doctor.
forall x: P(x) <-> Q(x). forall x: R(x) or Q(x). forall x: R(x) -> P(x). exists x: S(x). Therefore exists x: S(x) and P(x).