Is it permissible for a libero to serve as the playing captain?

The correct answer is that a libero is indeed allowed to serve as the playing captain. This aspect of volleyball rules recognizes the pivotal role of the libero in the game, as they are integral to the team's defense and overall performance.

The playing captain is responsible for communicating with the officials and making strategic decisions during the match. Allowing the libero to fill this role acknowledges their involvement and leadership on the court, despite their specialized position often being focused on defensive plays rather than typical front-row responsibilities.

The other options are misleading. The notion that they must be a different player misrepresents the rules governing positions and leadership roles in volleyball. Specifying that it can only occur in certain sets or only when the libero is on the court introduces unnecessary restrictions that do not align with the established rules, as the libero can serve as the captain at any time they are on the court.