Final answer:
In rural counties, the Sheriff option (c) is the elected official responsible for overseeing the operation of the jail, as opposed to other officials like county commissioners or the district attorney.
Step-by-step explanation:
In rural counties, the elected official who oversees the operation of the jail is the Sheriff. The sheriff's responsibilities typically include maintaining the peace and managing the county jail. This differs from other county officials like the mayor, county commissioners, and the district attorney who have other distinct roles within county government.
County commissioners often tackle the operation and administration of the broader scope of county functions, while the district attorney is involved with prosecuting crimes. The mayor's responsibilities can vary widely and are generally more focused on city governance rather than county operations.