Translate the following inference to logic notation: There is at least one x for which if z_3 plays tennis, then z_3 is a carpenter. For all x, z_3 will play tennis or z_3 is not a carpenter. Therefore there is at least one x for which z_3 is a carpenter if and only if z_3 will play tennis.
exists x: P(x) -> Q(x). forall x: P(x) or ~Q(x). Therefore exists x: Q(x) <-> P(x).