Consider the following premises. It is not sunny. Richard is playing squash if and only if William is happy. Richard is playing squash if and only if Jessica is writing a letter. Mary is making tea if and only if Jessica is writing a letter. Mary is making tea if and only if it is sunny. Can we infer the following from them? William is not happy.
 From the fact that Mary is making tea if and only if it is sunny, and that it is not sunny we can infer that Mary is not making tea. From the fact that Mary is making tea if and only if Jessica is writing a letter, and that Mary is not making tea we can infer that Jessica is not writing a letter. From the fact that Richard is playing squash if and only if Jessica is writing a letter, and that Jessica is not writing a letter we can infer that Richard is not playing squash. Finally, from the fact that Richard is playing squash if and only if William is happy, and that Richard is not playing squash we can infer that William is not happy. Therefore, the answer is yes.