Consider the following premises. Susan is running if and only if Mary is sleeping. Mary is sleeping or Joseph is happy. Susan is not running. Can we infer the following from them? It is raining or Joseph is happy.
 From the fact that Susan is running if and only if Mary is sleeping, and that Susan is not running we can infer that Mary is not sleeping. From the fact that Mary is not sleeping we can infer that Mary is not sleeping or it is raining. Finally, from the fact that Mary is not sleeping or it is raining, and that Mary is sleeping or Joseph is happy we can infer that it is raining or Joseph is happy. Therefore, the answer is yes.