Translate the following inference to logic notation: For all x, z_2 is a scientist or z_2 will not write a letter. For all x, if z_2 were a scientist, then z_2 is writing a letter. Therefore for all x, if z_2 writes a letter, then z_2 is a scientist.
forall x: P(x) or ~Q(x). forall x: P(x) -> Q(x). Therefore forall x: Q(x) -> P(x).