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At the end of "Batman: The Killing Joke", did Batman kill the Joker?

Yes, the Joker’s last joke made Batman break his principles and strangle the Joker to death with his own hands. This section has not been released. But you can understand that the Joker is not dead, because he continues to live in Batman's brain. The game Arkham Knight picks up the story after Batman strangles the Joker.