Translate the following inference to logic notation: For all x, if z_1 climbs a mountain, then z_1 is reading a book. For all x, if z_1 reads a book, then z_1 is climbing a mountain. There is at least one x for which z_1 will cook if and only if z_1 will climb a mountain. Therefore there is at least one x for which if z_1 reads a book, then z_1 is cooking.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). exists x: R(x) <-> P(x). Therefore exists x: Q(x) -> R(x).