Translate the following inference to logic notation: For all x, x_7 is a janitor if and only if x_7 will cook. There is at least one x for which if x_7 were a police officer, then x_7 is a writer. For all x, x_7 is a janitor or x_7 is a police officer. For all x, if x_7 cooks, then x_7 is a writer. Therefore there is at least one x for which x_7 is a writer.
forall x: P(x) <-> Q(x). exists x: R(x) -> S(x). forall x: P(x) or R(x). forall x: Q(x) -> S(x). Therefore exists x: S(x).