Translate the following inference to logic notation: For all x, if x_7 works, then x_7 is playing squash. For all x, if x_7 plays squash, then x_7 is working. There is at least one x for which if x_7 works, then x_7 is playing squash. Therefore there is at least one x for which x_7 will work if and only if x_7 will play squash.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). exists x: P(x) -> Q(x). Therefore exists x: P(x) <-> Q(x).