Consider the following premises. For all y, y is a doctor or y is not a writer. For all y, if y were a doctor, then y is a scientist. For all y, y is a writer if and only if y is a scientist. Can we infer the following from them? There is at least one y for which if is not true that y is a doctor if and only if y is a writer.
 From the fact that for all y, y is a doctor or y is not a writer we can infer that for all y, if y were a writer, then y is a doctor. From the fact that for all y, y is a writer if and only if y is a scientist we can infer that for all y, if y were a scientist, then y is a writer. From the fact that for all y, if y were a doctor, then y is a scientist, and that for all y, if y were a scientist, then y is a writer we can infer that for all y, if y were a doctor, then y is a writer. Finally, from the fact that for all y, if y were a doctor, then y is a writer, and that for all y, if y were a writer, then y is a doctor we can infer that for all y, y is a doctor if and only if y is a writer, which contradicts that There is at least one y for which if is not true that y is a doctor if and only if y is a writer. Therefore, the answer is no.