Translate the following inference to logic notation: For all x, x_10 is a soldier or x_10 will read a book. For all x, if x_10 reads a book, then x_10 is a lawyer. For all x, if x_10 were a lawyer, then x_10 is cooking. For all x, if x_10 were a soldier, then x_10 is cooking. There is at least one x for which x_10 will cook if and only if x_10 is a server. Therefore there is at least one x for which x_10 is a server.
forall x: P(x) or Q(x). forall x: Q(x) -> R(x). forall x: R(x) -> S(x). forall x: P(x) -> S(x). exists x: S(x) <-> T(x). Therefore exists x: T(x).