Consider the following premises. For all x, if x reads a book, then x is cooking. For all x, if x reads a book, then x is cooking. For all x, if x cooks, then x is reading a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which the fact that x reads a book does not imply that x is cooking.
 From the fact that for all x, if x reads a book, then x is cooking, and that for all x, if x cooks, then x is reading a book we can infer that for all x, x will read a book if and only if x will cook via universal biconditional introduction. From the fact that for all x, x will read a book if and only if x will cook we can infer that for all x, if x cooks, then x is reading a book via universal biconditional elimination. From the fact that for all x, if x cooks, then x is reading a book, and that for all x, if x reads a book, then x is cooking we can infer that for all x, x will cook if and only if x will read a book via universal biconditional introduction. Finally, from the fact that for all x, x will cook if and only if x will read a book we can infer that for all x, if x reads a book, then x is cooking via universal biconditional elimination, which contradicts that There is at least one x for which the fact that x reads a book does not imply that x is cooking. Therefore, the answer is no.