Translate the following inference to logic notation: For all x, if z plays squash, then z is a lawyer. There is at least one x for which z will write a letter or z will play squash. For all x, z will write a letter if and only if z is a lawyer. Therefore there is at least one x for which z is a lawyer.
forall x: P(x) -> Q(x). exists x: R(x) or P(x). forall x: R(x) <-> Q(x). Therefore exists x: Q(x).