Consider the following premises. Susan is running if and only if it is cold. It is overcast or Susan is not running. If Joseph plays tennis, then it is cold. Can we infer the following from them? The fact that Joseph plays tennis does not imply that it is overcast.
 From the fact that Susan is running if and only if it is cold we can infer that if it is cold, then Susan is running. From the fact that it is overcast or Susan is not running we can infer that if Susan goes running, then it is overcast. From the fact that if Joseph plays tennis, then it is cold, and that if it is cold, then Susan is running we can infer that if Joseph plays tennis, then Susan is running. Finally, from the fact that if Joseph plays tennis, then Susan is running, and that if Susan goes running, then it is overcast we can infer that if Joseph plays tennis, then it is overcast, which contradicts that The fact that Joseph plays tennis does not imply that it is overcast. Therefore, the answer is no.