Consider the following premises. If Patricia reads a book, then Thomas is not writing a letter. William is poor if and only if Patricia is reading a book. Thomas is writing a letter. John is a poet if and only if William is poor. Can we infer the following from them? John is a poet.
 From the fact that if Patricia reads a book, then Thomas is not writing a letter, and that Thomas is writing a letter we can infer that Patricia is not reading a book. From the fact that William is poor if and only if Patricia is reading a book, and that Patricia is not reading a book we can infer that William is not poor. Finally, from the fact that John is a poet if and only if William is poor, and that William is not poor we can infer that John is not a poet, which contradicts that John is a poet. Therefore, the answer is no.