Consider the following premises. It is raining or James is not a janitor. James is a janitor if and only if Joseph is sad. Can we infer the following from them? The fact that Joseph were sad does not imply that it is raining.
 From the fact that it is raining or James is not a janitor we can infer that if James were a janitor, then it is raining. From the fact that James is a janitor if and only if Joseph is sad we can infer that if Joseph were sad, then James is a janitor. Finally, from the fact that if Joseph were sad, then James is a janitor, and that if James were a janitor, then it is raining we can infer that if Joseph were sad, then it is raining, which contradicts that The fact that Joseph were sad does not imply that it is raining. Therefore, the answer is no.