Translate the following inference to logic notation: There is at least one x for which z will not write a letter. For all x, if z makes tea, then z is an office clerk. For all x, z will make tea or z is not an office clerk. For all x, z will write a letter if and only if z is an office clerk. Therefore there is at least one x for which z will not make tea.
exists x: ~P(x). forall x: Q(x) -> R(x). forall x: Q(x) or ~R(x). forall x: P(x) <-> R(x). Therefore exists x: ~Q(x).