Consider the following premises. If Jessica takes a plane, then William is happy. If William were happy, then Jessica is taking a plane. For all y_3, y_3 is not happy. Can we infer the following from them? If we can, name the inference rule being used: Jessica is not taking a plane or it is cloudy.
 From the fact that for all y_3, y_3 is not happy we can infer that William is not happy via universal instantiation. From the fact that if Jessica takes a plane, then William is happy, and that if William were happy, then Jessica is taking a plane we can infer that Jessica is taking a plane if and only if William is happy via biconditional introduction. From the fact that Jessica is taking a plane if and only if William is happy, and that William is not happy we can infer that Jessica is not taking a plane via biconditional elimination. Finally, from the fact that Jessica is not taking a plane we can infer that Jessica is not taking a plane or it is cloudy via addition. Therefore, the answer is yes.