Consider the following premises. For all x_7, x_7 will take a plane. For all x_7, x_7 will take a plane if and only if x_7 is a politician. For all x_7, x_7 is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which either x_7 is a politician or x_7 is sad are not true.
 From the fact that for all x_7, x_7 will take a plane if and only if x_7 is a politician we can infer that for all x_7, if x_7 takes a plane, then x_7 is a politician via universal biconditional elimination. From the fact that for all x_7, if x_7 takes a plane, then x_7 is a politician, and that for all x_7, x_7 will take a plane we can infer that for all x_7, x_7 is a politician via universal modus ponens. Finally, from the fact that for all x_7, x_7 is a politician, and that for all x_7, x_7 is sad we can infer that for all x_7, x_7 is a politician and x_7 is sad via universal conjunction, which contradicts that There is at least one x_7 for which either x_7 is a politician or x_7 is sad are not true. Therefore, the answer is no.