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