“Wile E. Coyote was the Roadrunner’s nemesis, not Bugs Bunny’s nemesis. Elmer Fudd was Bug’s nemesis.”
But in this case, the cartoon actually features Bugs and Wile E. Google Operation Rabbit. It is on YouTube. See the whole thing.
http://www.youtube.com/watch?v=SoKA2OLJ8hs