Translate the following inference to logic notation: There is at least one x for which if z reads a book, then z is cooking. For all x, if z reads a book, then z is cooking. For all x, if z cooks, then z is reading a book. Therefore there is at least one x for which if z reads a book, then z is cooking.
exists x: P(x) -> Q(x). forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore exists x: P(x) -> Q(x).