Consider the following premises. If Michael were sad, then it is overcast. If it is overcast, then Michael is sad. Michael is sad if and only if Patricia is playing tennis. Can we infer the following from them? The fact that it is overcast does not imply that Patricia is playing tennis.
 From the fact that if it is overcast, then Michael is sad, and that if Michael were sad, then it is overcast we can infer that it is overcast if and only if Michael is sad. From the fact that Michael is sad if and only if Patricia is playing tennis we can infer that if Michael were sad, then Patricia is playing tennis. From the fact that it is overcast if and only if Michael is sad we can infer that if it is overcast, then Michael is sad. Finally, from the fact that if it is overcast, then Michael is sad, and that if Michael were sad, then Patricia is playing tennis we can infer that if it is overcast, then Patricia is playing tennis, which contradicts that The fact that it is overcast does not imply that Patricia is playing tennis. Therefore, the answer is no.