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