Consider the following premises. Michael is playing a game or David is an electrician. If David were an electrician, then it is raining. If Michael plays a game, then it is raining. Patricia is happy if and only if it is raining. Can we infer the following from them? If we can, name the inference rule being used: Patricia is not happy.
 From the fact that if Michael plays a game, then it is raining, that if David were an electrician, then it is raining, and that Michael is playing a game or David is an electrician we can infer that it is raining via disjunction elimination. From the fact that Patricia is happy if and only if it is raining we can infer that if it rains, then Patricia is happy via biconditional elimination. Finally, from the fact that if it rains, then Patricia is happy, and that it is raining we can infer that Patricia is happy via modus ponens, which contradicts that Patricia is not happy. Therefore, the answer is no.