Translate the following inference to logic notation: There is at least one x for which if z reads a book, then z is poor. For all x, if z were happy, then z is reading a book. For all x, z is poor if and only if z will make tea. Therefore there is at least one x for which if z were happy, then z is making tea.
exists x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: Q(x) <-> S(x). Therefore exists x: R(x) -> S(x).