Consider the following premises. If Linda were not a politician, then Mary is making tea. Linda is a politician if and only if Karen is climbing a mountain. Karen is not climbing a mountain. Can we infer the following from them? Mary is making tea.
 From the fact that Linda is a politician if and only if Karen is climbing a mountain, and that Karen is not climbing a mountain we can infer that Linda is not a politician. Finally, from the fact that if Linda were not a politician, then Mary is making tea, and that Linda is not a politician we can infer that Mary is making tea. Therefore, the answer is yes.