Translate the following inference to logic notation: For all x, if x_1 plays tennis, then x_1 is sleeping. For all x, x_1 will play tennis if and only if x_1 will climb a mountain. For all x, if x_1 sleeps, then x_1 is climbing a mountain. For all x, if x_1 climbs a mountain, then x_1 is playing tennis. Therefore for all x, x_1 will play tennis if and only if x_1 will climb a mountain.
forall x: P(x) -> Q(x). forall x: P(x) <-> R(x). forall x: Q(x) -> R(x). forall x: R(x) -> P(x). Therefore forall x: P(x) <-> R(x).