Consider the following premises. Barbara is writing a letter. If it rains, then Barbara is not writing a letter. Joseph is not a server or Karen is making tea. Joseph is a server or it is raining. Can we infer the following from them? Karen is making tea.
 From the fact that Joseph is a server or it is raining, and that Joseph is not a server or Karen is making tea we can infer that it is raining or Karen is making tea. From the fact that if it rains, then Barbara is not writing a letter, and that Barbara is writing a letter we can infer that it is not raining. Finally, from the fact that it is raining or Karen is making tea, and that it is not raining we can infer that Karen is making tea. Therefore, the answer is yes.