Consider the following premises. Barbara is a sailor if and only if Charles is drinking water. If Patricia were an astronaut, then Barbara is a sailor. Charles is not drinking water. Can we infer the following from them? If we can, name the inference rule being used: Patricia is an astronaut.
 From the fact that Barbara is a sailor if and only if Charles is drinking water we can infer that if Barbara were a sailor, then Charles is drinking water via biconditional elimination. From the fact that if Patricia were an astronaut, then Barbara is a sailor, and that if Barbara were a sailor, then Charles is drinking water we can infer that if Patricia were an astronaut, then Charles is drinking water via transitivity. Finally, from the fact that if Patricia were an astronaut, then Charles is drinking water, and that Charles is not drinking water we can infer that Patricia is not an astronaut via modus tollens, which contradicts that Patricia is an astronaut. Therefore, the answer is no.