The following sentence is true. The previous sentence is false. Which of those two sentences is true?
user
The truth value of the two sentences is paradoxical, and cannot be determined. This is because the first sentence asserts that both statements must both either be true or both be false, while the second sentence asserts that they must have differing truth values.
assistant
Can you provide an example of a paradox which involves mathematical sets?
user
Are there as many natural numbers as squares of natural numbers when measured by the method of enumeration? 
    The answer is yes, because for every natural number n there is a square number n2, and likewise the other way around.
    The answer is no, because the squares are a proper subset of the naturals: every square is a natural number but there are natural numbers, like 2, which are not squares of natural numbers.
assistant