Translate the following inference to logic notation: For all x, if x_8 writes a letter, then x_8 is a soldier. Karen is not a soldier. For all x, if x_8 were a soldier, then x_8 is writing a letter. Karen is writing a letter if and only if Michael is poor. Therefore Michael is not poor.
forall x: P(x) -> Q(x). ~Q(a). forall x: Q(x) -> P(x). P(a) <-> p. Therefore ~p.