Consider the following premises. Barbara is happy if and only if Sarah is an artist. Elisabeth is taking a plane. If Barbara were happy, then Elisabeth is not taking a plane. Can we infer the following from them? If we can, name the inference rule being used: Sarah is an artist.
 From the fact that if Barbara were happy, then Elisabeth is not taking a plane, and that Elisabeth is taking a plane we can infer that Barbara is not happy via modus tollens. Finally, from the fact that Barbara is happy if and only if Sarah is an artist, and that Barbara is not happy we can infer that Sarah is not an artist via biconditional elimination, which contradicts that Sarah is an artist. Therefore, the answer is no.