Translate the following inference to logic notation: For all x, if x_7 writes a letter, then x_7 is a sailor. For all x, if x_7 were a sailor, then x_7 is writing a letter. There is at least one x for which x_7 is not a nurse. For all x, x_7 is a nurse if and only if x_7 will write a letter. Therefore there is at least one x for which x_7 is not a sailor.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). exists x: ~R(x). forall x: R(x) <-> P(x). Therefore exists x: ~Q(x).