Consider the following premises. Elisabeth is happy if and only if John is a politician. For all x_15, if x_15 were a politician, then x_15 is writing a letter. For all x_15, x_15 will not write a letter. Can we infer the following from them? Elisabeth is not happy or Mary is poor.
 From the fact that for all x_15, if x_15 were a politician, then x_15 is writing a letter, and that for all x_15, x_15 will not write a letter we can infer that for all x_15, x_15 is not a politician. From the fact that for all x_15, x_15 is not a politician we can infer that John is not a politician. From the fact that Elisabeth is happy if and only if John is a politician, and that John is not a politician we can infer that Elisabeth is not happy. Finally, from the fact that Elisabeth is not happy we can infer that Elisabeth is not happy or Mary is poor. Therefore, the answer is yes.