Translate the following inference to logic notation: There is at least one x for which if x_2 were a doctor, then x_2 is writing a letter. For all x, x_2 is not a carpenter. For all x, x_2 is a carpenter or x_2 is a doctor. Therefore there is at least one x for which x_2 will write a letter.
exists x: P(x) -> Q(x). forall x: ~R(x). forall x: R(x) or P(x). Therefore exists x: Q(x).