Consider the following premises. William is a sailor if and only if Richard is cooking. Patricia is climbing a mountain. If William were a sailor, then Patricia is not climbing a mountain. Can we infer the following from them? Richard is not cooking.
 From the fact that if William were a sailor, then Patricia is not climbing a mountain, and that Patricia is climbing a mountain we can infer that William is not a sailor. From the fact that William is a sailor if and only if Richard is cooking we can infer that if Richard cooks, then William is a sailor. Finally, from the fact that if Richard cooks, then William is a sailor, and that William is not a sailor we can infer that Richard is not cooking. Therefore, the answer is yes.