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