Compare/contrast the relationship the King and Queen have with Rosencrantz and Guildenstern, to the relationship Hamlet has with them.

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The King and Queen pretend to be cordial with Rosencrantz and Guildenstern, pretend to be happy to welcome them to Denmark but their relationship is based on the utility that they think they can derive from the friendship between R and G and Hamlet.  There isn't a great deal of substance to their relationship, particularly once it becomes clear that their utility is limited because Hamlet sees through them.

Of course Hamlet questions their motives before they've even spoken with the King about the reason for their summons.  At first he plays along with them but grows more and more distant and abusive as it becomes clear that they are there to spy on him.  The scene where they come to summon him to his mother's room after the Mousetrap demonstrate the absolute disdain he feels towards them as well as a possible sense of betrayal and hurt.

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