Consider the following premises. For all y, y is not bored. If William plays tennis, then Patricia is happy. Joseph is bored if and only if William is playing tennis. If Patricia were happy, then William is playing tennis. Can we infer the following from them? Patricia is not happy.
 From the fact that if Patricia were happy, then William is playing tennis, and that if William plays tennis, then Patricia is happy we can infer that Patricia is happy if and only if William is playing tennis. From the fact that for all y, y is not bored we can infer that Joseph is not bored. From the fact that Joseph is bored if and only if William is playing tennis, and that Joseph is not bored we can infer that William is not playing tennis. Finally, from the fact that Patricia is happy if and only if William is playing tennis, and that William is not playing tennis we can infer that Patricia is not happy. Therefore, the answer is yes.