Question

what does claudius want the english ruler to do with hamlet? do rosencratz and guildenstern know that?
to trap him there; yes
to trick him into marrying one of his daughters; probably not
to kill him; probably not
to kill him; yes they do

Explanation:

In Shakespeare's Hamlet, Claudius sends Hamlet to England with a secret letter ordering the English ruler to execute Hamlet. Rosencrantz and Guildenstern are told they are accompanying Hamlet to ensure his safety/remove him from Denmark, and they are not aware of the deadly secret order, so they likely do not know the true intent to kill Hamlet.

Answer:

Green: To kill him; probably not