Suppose somebody asks you to play two truths and a lie. In order to humor them, you come up with a logical puzzle under a bivalent truth assignment and the natural English language meaning of 'One of ...' as greater than or equal to one. Indeed:
One of these statements is true.
One of these statements is false.
X.
This actually satisfies the requirement of our problem. You can see that by assuming that X were true, this would force the first statement true, and either assignment to the second yields a contradiction. Therefore, X must be false, so the second is true, and the first is therefore true as well.