Translate the following inference to logic notation: For all x, if y_2 were a politician, then y_2 is making tea. For all x, if y_2 makes tea, then y_2 is cooking. There is at least one x for which if y_2 cooks, then y_2 is a politician. Therefore there is at least one x for which if y_2 makes tea, then y_2 is a politician.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). exists x: R(x) -> P(x). Therefore exists x: Q(x) -> P(x).