Consider the following premises. Joseph is rich. If it is overcast, then Joseph is not rich. Susan is writing a letter if and only if it is overcast. For all x_10, if x_10 were a scientist, then x_10 is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: Susan is not a scientist.
 From the fact that if it is overcast, then Joseph is not rich, and that Joseph is rich we can infer that it is not overcast via modus tollens. From the fact that for all x_10, if x_10 were a scientist, then x_10 is writing a letter we can infer that if Susan were a scientist, then Susan is writing a letter via universal instantiation. From the fact that Susan is writing a letter if and only if it is overcast, and that it is not overcast we can infer that Susan is not writing a letter via biconditional elimination. Finally, from the fact that if Susan were a scientist, then Susan is writing a letter, and that Susan is not writing a letter we can infer that Susan is not a scientist via modus tollens. Therefore, the answer is yes.