Consider the following premises. Barbara is playing tennis if and only if Patricia is climbing a mountain. Patricia is climbing a mountain if and only if it is late. Can we infer the following from them? If it is late, then Barbara is playing tennis.
 From the fact that Patricia is climbing a mountain if and only if it is late we can infer that if it is late, then Patricia is climbing a mountain. From the fact that Barbara is playing tennis if and only if Patricia is climbing a mountain we can infer that if Patricia climbs a mountain, then Barbara is playing tennis. Finally, from the fact that if it is late, then Patricia is climbing a mountain, and that if Patricia climbs a mountain, then Barbara is playing tennis we can infer that if it is late, then Barbara is playing tennis. Therefore, the answer is yes.