Ask one what the other will say is behind their door.

If A tells the truth then B tells the lie. If paradise is behind B then A will say that B will say that B leads to death. If death is behind B then A will say that B will say that B leads to paradise.

If A tells the lie then B tells the truth. If paradise is behind B then A will say that B will say that B leads to death. If death is behind B then A will say that B will say that B leads to paradise.

In all cases the door which is claimed to be paradise is the door to death and the door which is claimed to be death is the door to paradise.

You need to meet Raymond Smullyan. He is dead, but his puzzle books are available with many doors in many configurations with tigers or princesses behind them and whole islands of truth tellers, liars and annoying people who do a bit of each...

Dover: No conversation would be complete without asking for a few of your jokes or some wordplay. Usually, I don't have to ask!
Raymond Smullyan: I'd be delighted. Amongst my favorite jokes are:
(1) A physicist visited a mathematician friend and told him that he just concluded an experiment that conclusively proves that quantity A is bigger than quantity B. The mathematician replied, "That's perfectly understandable! You didn't even have to make the experiment. A must be bigger than B for the following reasons . . ." The physicist interrupted him and said, "Oh I made a mistake. It is not A that is bigger than B; it is B that is bigger than A." The mathematician said, "That's even more understandable because . . ."
(2) A man went into a restaurant and said to the waiter: "I would like some coffee without cream." The waiter went into the kitchen and returned and said, "I am sorry, Sir, we don't have any cream. I can let you have coffee without milk."
(3) In Ireland a man went into a bar and ordered three beers. Night after night he would order three beers. At one point the bartender asked him why he always ordered three, and the man explained that he had two brothers, one in America and one in Australia, and they made a pact that each time one of them would drink a beer, he would also drink two others in memory of his two brothers. This went on night after night for several months, and many of the customers were quite touched by this. Then one night, to everyone's amazement and sorrow, the man ordered only two beers. Finally one man came over to him to offer his condolences for the death of his brother. To his surprise, the man told him that both his brothers were alive and quite well. When asked why he then ordered only two beers, the man replied: "I decided to stop drinking."

https://www.doverpublications.com/raymondsmullyan/

Thank you for the comments, and of course the solution. I will check out Raymond Smullyan and I love the Irish joke! Most lightening!

I can't help but think this equation above has a relation to both Buddhist negation, and mathematically truth tables. Does anyone else see a coloration?