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