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They cannot be both false (for other reasons).

Assuming both are false, there isn't $1mil in either of the boxes, and according to the sign on box B, box A doesn't contain a snake - but each box has either or, hence it's a contradiction, and we were wrong in our assumption.

So both are true.

edit: These riddles remind me that they should still release at least the second in the Professor Layton series :/

 

Maybe the question should have been "Would you open a box at all, and if so, which", would make it trickier.