Translate the following inference to logic notation: There is at least one x for which if x plays tennis, then x is a doctor. For all x, x is a doctor if and only if x will play tennis. Therefore there is at least one x for which x is a doctor if and only if x will play tennis.
exists x: P(x) -> Q(x). forall x: Q(x) <-> P(x). Therefore exists x: Q(x) <-> P(x).