Consider the following premises. For all z, z will write a letter if and only if z is a scientist. For all z, z will play a game if and only if z will take a plane. For all z, z will play a game if and only if z is a scientist. For all z, z will not take a plane. Can we infer the following from them? There is at least one z for which z will write a letter.
 From the fact that for all z, z will play a game if and only if z will take a plane, and that for all z, z will not take a plane we can infer that for all z, z will not play a game. From the fact that for all z, z will play a game if and only if z is a scientist, and that for all z, z will not play a game we can infer that for all z, z is not a scientist. Finally, from the fact that for all z, z will write a letter if and only if z is a scientist, and that for all z, z is not a scientist we can infer that for all z, z will not write a letter, which contradicts that There is at least one z for which z will write a letter. Therefore, the answer is no.