Translate the following inference to logic notation: For all x, if x_5 plays tennis, then x_5 is a carpenter. For all x, if x_5 were a carpenter, then x_5 is playing tennis. For all x, if x_5 plays tennis, then x_5 is a carpenter. Therefore for all x, x_5 is a carpenter if and only if x_5 will play tennis.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: P(x) -> Q(x). Therefore forall x: Q(x) <-> P(x).