Translate the following inference to logic notation: For all x, x_9 is excited if and only if x_9 will write a letter. For all x, if x_9 were excited, then x_9 is writing a letter. For all x, x_9 will not write a letter. There is at least one x for which x_9 is excited if and only if x_9 will drink water. Therefore there is at least one x for which x_9 will not drink water.
forall x: P(x) <-> Q(x). forall x: P(x) -> Q(x). forall x: ~Q(x). exists x: P(x) <-> R(x). Therefore exists x: ~R(x).