Translate the following inference to logic notation: For all x, x_6 is a server if and only if x_6 will cook. There is at least one x for which if x_6 were a server, then x_6 is cooking. Therefore there is at least one x for which if x_6 were a server, then x_6 is cooking.
forall x: P(x) <-> Q(x). exists x: P(x) -> Q(x). Therefore exists x: P(x) -> Q(x).