Translate the following inference to logic notation: There is at least one x for which x_9 will go running if and only if x_9 will make tea. For all x, x_9 will go running if and only if x_9 is fast. Therefore there is at least one x for which if x_9 makes tea, then x_9 is fast.
exists x: P(x) <-> Q(x). forall x: P(x) <-> R(x). Therefore exists x: Q(x) -> R(x).