Consider the following premises. It is not late. If it is cloudy, then Jessica is a mechanic. Joseph is writing a letter if and only if it is late. Jessica is not a mechanic. Can we infer the following from them? If we can, name the inference rule being used: It is not cloudy and Joseph is not writing a letter.
 From the fact that if it is cloudy, then Jessica is a mechanic, and that Jessica is not a mechanic we can infer that it is not cloudy via modus tollens. From the fact that Joseph is writing a letter if and only if it is late, and that it is not late we can infer that Joseph is not writing a letter via biconditional elimination. Finally, from the fact that it is not cloudy, and that Joseph is not writing a letter we can infer that it is not cloudy and Joseph is not writing a letter via conjunction. Therefore, the answer is yes.