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