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