Consider the following premises. If Jessica reads a book, then Susan is a carpenter. Susan is a carpenter if and only if Jessica is reading a book. If Jessica reads a book, then Susan is a carpenter. Can we infer the following from them? Jessica is reading a book if and only if Susan is a carpenter.
 From the fact that Susan is a carpenter if and only if Jessica is reading a book we can infer that if Susan were a carpenter, then Jessica is reading a book. Finally, from the fact that if Jessica reads a book, then Susan is a carpenter, and that if Susan were a carpenter, then Jessica is reading a book we can infer that Jessica is reading a book if and only if Susan is a carpenter. Therefore, the answer is yes.