Translate the following inference to logic notation: For all x, if x_4 plays squash, then x_4 is a doctor. For all x, if x_4 were a doctor, then x_4 is playing squash. If Jessica plays squash, then Joseph is a soldier. Therefore if Jessica were a doctor, then Joseph is a soldier.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). P(a) -> p. Therefore Q(a) -> p.