Consider the following premises. Joseph is not an electrician if and only if it is raining. James is playing squash if and only if James is cooking. If Joseph were an electrician, then James is cooking. James is not playing squash. Can we infer the following from them? If we can, name the inference rule being used: It is not raining.
 From the fact that James is playing squash if and only if James is cooking we can infer that if James cooks, then James is playing squash via biconditional elimination. From the fact that if Joseph were an electrician, then James is cooking, and that if James cooks, then James is playing squash we can infer that if Joseph were an electrician, then James is playing squash via transitivity. From the fact that if Joseph were an electrician, then James is playing squash, and that James is not playing squash we can infer that Joseph is not an electrician via modus tollens. From the fact that Joseph is not an electrician if and only if it is raining we can infer that if Joseph were not an electrician, then it is raining via biconditional elimination. Finally, from the fact that if Joseph were not an electrician, then it is raining, and that Joseph is not an electrician we can infer that it is raining via modus ponens, which contradicts that It is not raining. Therefore, the answer is no.