Translate the following inference to logic notation: There is at least one x for which if x_5 were a lawyer, then x_5 is reading a book. For all x, if x_5 reads a book, then x_5 is running. For all x, if x_5 were a mechanic, then x_5 is a lawyer. For all x, if x_5 goes running, then x_5 is a mechanic. Therefore there is at least one x for which x_5 will read a book if and only if x_5 is a lawyer.
exists x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: S(x) -> P(x). forall x: R(x) -> S(x). Therefore exists x: Q(x) <-> P(x).