Translate the following inference to logic notation: For all x, x is an astronaut if and only if x is a lawyer. For all x, if x reads a book, then x is an astronaut. There is at least one x for which if x cooks, then x is reading a book. Therefore there is at least one x for which if x cooks, then x is a lawyer.
forall x: P(x) <-> Q(x). forall x: R(x) -> P(x). exists x: S(x) -> R(x). Therefore exists x: S(x) -> Q(x).