Translate the following inference to logic notation: There is at least one x for which x_6 will write a letter if and only if x_6 is a lawyer. For all x, x_6 will not write a letter. For all x, if x_6 were a lawyer, then x_6 is writing a letter. Therefore there is at least one x for which x_6 is not a lawyer.
exists x: P(x) <-> Q(x). forall x: ~P(x). forall x: Q(x) -> P(x). Therefore exists x: ~Q(x).