Consider the following premises. For all x_2, x_2 will play a game or x_2 will make tea. There is at least one x_2 for which x_2 will go running. For all x_2, x_2 will not play a game. Can we infer the following from them? For all x_2, either x_2 will make tea or x_2 will go running are not true.
 From the fact that for all x_2, x_2 will play a game or x_2 will make tea, and that for all x_2, x_2 will not play a game we can infer that for all x_2, x_2 will make tea. Finally, from the fact that for all x_2, x_2 will make tea, and that there is at least one x_2 for which x_2 will go running we can infer that there is at least one x_2 for which x_2 will make tea and x_2 will go running, which contradicts that For all x_2, either x_2 will make tea or x_2 will go running are not true. Therefore, the answer is no.