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Rosencrantz and Guildenstern are Hamlet's childhood friends. Claudius sends them to spy on Hamlet.
These would be Rosencrantz and Guildenstern, who are actually spies for the king.
Primarily, spying on Hamlet.
No; they are more than happy to serve the king.
He's the king. A subject should obey his king.
Hamlet changes the letter going to the King of England to kill him when he gets there to say to kill the people who give you this letter,which were Rosencrantz and Guildenstern. So they were killed instead.
Claudius and Gertrude set Rosencrantz and Guildenstern to spy on Hamlet to discover the cause of his apparent madness
Rosencrantz and Guildenstern are old school buddies of Hamlet's. They have been hired by the king to spy on Hamlet to find out why he is acting so peculiarly.
The king and queen want them to cozy up to Hamlet and find out what's troubling him.
In Tom Stoppard's play, Rosencrantz and Guildenstern Are Dead, Ros and Guil have a difficult time remembering their own names. They know they are one of Rosencrantz or Guildenstern, but are not sure which. Viewers of Shakespeare's Hamlet often have a similar problem, as does King Claudius, although the characters themselves seem to be clear on the issue in the Shakespeare play.
True. Hamlet changed the king's orders to the English from "Kill Hamlet" to "Kill Rosencrantz and Guildenstern." He didn't have to do that; he could have changed the orders to "Give Hamlet some flowers".
They were sent for specifically to spy on Hamlet and report to the king and queen. Spies generally do not like the people they are spying on to know it. Rosencrantz and Guildenstern would have an easier time getting unguarded admissions from Hamlet if they were not "outed".