Translate the following inference to logic notation: For all x, if x works, then x is cooking. There is at least one x for which if x works, then x is taking a plane. For all x, x will cook if and only if x will take a plane. For all x, if x takes a plane, then x is working. Therefore there is at least one x for which x will take a plane if and only if x will work.
forall x: P(x) -> Q(x). exists x: P(x) -> R(x). forall x: Q(x) <-> R(x). forall x: R(x) -> P(x). Therefore exists x: R(x) <-> P(x).