Consider the following premises. There is at least one y for which y will play a game or y will not write a letter. For all y, y will write a letter. For all y, if y makes tea, then y is playing a game. For all y, y is a sailor. Can we infer the following from them? For all y, either y is a sailor or y will play a game are not true.
 From the fact that there is at least one y for which y will play a game or y will not write a letter we can infer that there is at least one y for which if y writes a letter, then y is playing a game. From the fact that for all y, y will write a letter we can infer that for all y, y will write a letter or y will make tea. From the fact that there is at least one y for which if y writes a letter, then y is playing a game, that for all y, if y makes tea, then y is playing a game, and that for all y, y will write a letter or y will make tea we can infer that there is at least one y for which y will play a game. Finally, from the fact that for all y, y is a sailor, and that there is at least one y for which y will play a game we can infer that some sailors will play a game, which contradicts that For all y, either y is a sailor or y will play a game are not true. Therefore, the answer is no.