Consider the following premises. If Jessica climbs a mountain, then Patricia is reading a book. For all x_2, x_2 will climb a mountain if and only if x_2 is a poet. Patricia is not reading a book. Can we infer the following from them? Jessica is a poet.
 From the fact that for all x_2, x_2 will climb a mountain if and only if x_2 is a poet we can infer that Jessica is climbing a mountain if and only if Jessica is a poet. From the fact that Jessica is climbing a mountain if and only if Jessica is a poet we can infer that if Jessica were a poet, then Jessica is climbing a mountain. From the fact that if Jessica were a poet, then Jessica is climbing a mountain, and that if Jessica climbs a mountain, then Patricia is reading a book we can infer that if Jessica were a poet, then Patricia is reading a book. Finally, from the fact that if Jessica were a poet, then Patricia is reading a book, and that Patricia is not reading a book we can infer that Jessica is not a poet, which contradicts that Jessica is a poet. Therefore, the answer is no.