Consider the following premises. It is not overcast. Patricia is not sleeping. Patricia is sleeping if and only if Patricia is an astronaut. If Richard were bored, then it is overcast. Can we infer the following from them? If we can, name the inference rule being used: Richard is not bored and Patricia is not an astronaut.
 From the fact that if Richard were bored, then it is overcast, and that it is not overcast we can infer that Richard is not bored via modus tollens. From the fact that Patricia is sleeping if and only if Patricia is an astronaut, and that Patricia is not sleeping we can infer that Patricia is not an astronaut via biconditional elimination. Finally, from the fact that Richard is not bored, and that Patricia is not an astronaut we can infer that Richard is not bored and Patricia is not an astronaut via conjunction. Therefore, the answer is yes.