Consider the following premises. If Elisabeth were rich, then Charles is a scientist. If James goes running, then Elisabeth is rich. If Charles were a scientist, then Elisabeth is rich. James is running or Joseph is not writing a letter. Can we infer the following from them? The fact that Joseph writes a letter does not imply that Charles is a scientist.
 From the fact that if Elisabeth were rich, then Charles is a scientist, and that if Charles were a scientist, then Elisabeth is rich we can infer that Elisabeth is rich if and only if Charles is a scientist. From the fact that Elisabeth is rich if and only if Charles is a scientist we can infer that if Elisabeth were rich, then Charles is a scientist. From the fact that James is running or Joseph is not writing a letter we can infer that if Joseph writes a letter, then James is running. From the fact that if Joseph writes a letter, then James is running, and that if James goes running, then Elisabeth is rich we can infer that if Joseph writes a letter, then Elisabeth is rich. Finally, from the fact that if Joseph writes a letter, then Elisabeth is rich, and that if Elisabeth were rich, then Charles is a scientist we can infer that if Joseph writes a letter, then Charles is a scientist, which contradicts that The fact that Joseph writes a letter does not imply that Charles is a scientist. Therefore, the answer is no.