Consider the following premises. If Patricia reads a book, then Robert is bored. Robert is bored if and only if it is raining. If it is late, then Patricia is reading a book. If Patricia reads a book, then it is late. It is not raining. Can we infer the following from them? If we can, name the inference rule being used: It is late.
 From the fact that Robert is bored if and only if it is raining, and that it is not raining we can infer that Robert is not bored via biconditional elimination. From the fact that if Patricia reads a book, then Robert is bored, and that Robert is not bored we can infer that Patricia is not reading a book via modus tollens. From the fact that if Patricia reads a book, then it is late, and that if it is late, then Patricia is reading a book we can infer that Patricia is reading a book if and only if it is late via biconditional introduction. Finally, from the fact that Patricia is reading a book if and only if it is late, and that Patricia is not reading a book we can infer that it is not late via biconditional elimination, which contradicts that It is late. Therefore, the answer is no.