Final answer:
The theme developed through Hamlet's interactions with Rosencrantz and Guildenstern is loyalty, as they betray Hamlet by spying on him, highlighting their disloyalty.
Step-by-step explanation:
The theme that is developed and questioned through the interaction of Hamlet with Rosencrantz and Guildenstern is loyalty. In William Shakespeare's play, 'Hamlet,' these characters are school friends of Hamlet who are summoned by King Claudius to spy on the prince, thereby betraying their friendship.
Many themes run through 'Hamlet,' including those of guilt, jealousy, and greed, but the interactions with Rosencrantz and Guildenstern particularly explore and challenge the idea of loyalty. Hamlet, feeling isolated and betrayed, uses his interactions to test their truthfulness and ultimately confirms their disloyalty. Thus, the correct answer to the question is C.) loyalty.