Consider the following premises. If Jennifer were a poet, then Patricia is a politician. For all x_10, x_10 will write a letter. For all x_10, if x_10 writes a letter, then x_10 is a poet. Can we infer the following from them? If we can, name the inference rule being used: Patricia is not a politician.
 From the fact that for all x_10, if x_10 writes a letter, then x_10 is a poet, and that for all x_10, x_10 will write a letter we can infer that for all x_10, x_10 is a poet via universal modus ponens. From the fact that for all x_10, x_10 is a poet we can infer that Jennifer is a poet via universal instantiation. Finally, from the fact that if Jennifer were a poet, then Patricia is a politician, and that Jennifer is a poet we can infer that Patricia is a politician via modus ponens, which contradicts that Patricia is not a politician. Therefore, the answer is no.