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