Translate the following inference to logic notation: For all x, if x_13 were a politician, then x_13 is writing a letter. For all x, x_13 is a politician if and only if x_13 is an office clerk. There is at least one x for which x_13 is not an office clerk. For all x, x_13 is a politician if and only if x_13 will write a letter. Therefore there is at least one x for which x_13 will not write a letter.
forall x: P(x) -> Q(x). forall x: P(x) <-> R(x). exists x: ~R(x). forall x: P(x) <-> Q(x). Therefore exists x: ~Q(x).