Translate the following inference to logic notation: For all x, x_1 will read a book if and only if x_1 will climb a mountain. For all x, if x_1 works, then x_1 is a scientist. There is at least one x for which if x_1 climbs a mountain, then x_1 is working. Therefore there is at least one x for which if x_1 reads a book, then x_1 is a scientist.
forall x: P(x) <-> Q(x). forall x: R(x) -> S(x). exists x: Q(x) -> R(x). Therefore exists x: P(x) -> S(x).