Consider the following premises. Elisabeth is taking a plane. Mary is a politician if and only if John is drinking water. Mary is a politician. Can we infer the following from them? If we can, name the inference rule being used: John is not drinking water.
 From the fact that Mary is a politician if and only if John is drinking water we can infer that if Mary were a politician, then John is drinking water via biconditional elimination. Finally, from the fact that if Mary were a politician, then John is drinking water, and that Mary is a politician we can infer that John is drinking water via modus ponens, which contradicts that John is not drinking water. Therefore, the answer is no.