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