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