Translate the following inference to logic notation: For all x, if x_12 were a doctor, then x_12 is a poet. Linda is poor. If David were a poet, then Linda is not poor. If David were a poet, then David is a doctor. Therefore David is not a doctor.
forall x: P(x) -> Q(x). p. Q(a) -> ~p. Q(a) -> P(a). Therefore ~P(a).