Translate the following inference to logic notation: For all x, if y_1 plays tennis, then y_1 is a poet. There is at least one x for which if y_1 were a poet, then y_1 is playing tennis. Therefore there is at least one x for which if y_1 were a poet, then y_1 is playing tennis.
forall x: P(x) -> Q(x). exists x: Q(x) -> P(x). Therefore exists x: Q(x) -> P(x).