Consider the following premises. If it is cloudy, then Patricia is reading a book. If Patricia reads a book, then Mary is playing tennis. If Mary plays tennis, then it is cloudy. If it is windy, then it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: The fact that it is windy does not imply that Patricia is reading a book.
 From the fact that if Patricia reads a book, then Mary is playing tennis, and that if Mary plays tennis, then it is cloudy we can infer that if Patricia reads a book, then it is cloudy via transitivity. From the fact that if Patricia reads a book, then it is cloudy, and that if it is cloudy, then Patricia is reading a book we can infer that Patricia is reading a book if and only if it is cloudy via biconditional introduction. From the fact that Patricia is reading a book if and only if it is cloudy we can infer that if it is cloudy, then Patricia is reading a book via biconditional elimination. Finally, from the fact that if it is windy, then it is cloudy, and that if it is cloudy, then Patricia is reading a book we can infer that if it is windy, then Patricia is reading a book via transitivity, which contradicts that The fact that it is windy does not imply that Patricia is reading a book. Therefore, the answer is no.