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Not necessary
Without defining a particular mapping (i.e. language or convention) it would be just as easy to define it the other way round.
So suppose 0 is true and 1 is false.
Since the reply is 1, that means it's false. Which means that the mapping is wrong. Which means that 1 is true and 0 is false. Which is a contradiction since we assumed it otherwise. Which proves that I'm utterly bored. QED.
Agree!!!!
joke/meme