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