Translate the following inference to logic notation: For all x, if y goes running, then y is an office clerk. For all x, if y were an office clerk, then y is running. There is at least one x for which if y goes running, then y is an office clerk. Therefore there is at least one x for which y will go running if and only if y is an office clerk.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). exists x: P(x) -> Q(x). Therefore exists x: P(x) <-> Q(x).