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2. Which of the following has an el llowing has an element that is less than any other element in that set? I. The set of pos
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Answer #1

The reason why I is false is simply that there is no such thing as the smallest positive rational number. Between any two positive rational numbers, there is another one. So you cannot find a such a smallest element in I.

For II, there is no smallest positive rational number r that r² ≥ 2. The smallest such real number would be √2, but that isn't a rational number; it's irrational.

For III, there is no smallest positive rational number r that r > 4. 2 would not work because 2² = 4, and 4 = 4 not that 4 > 4.

Hence, None is correct.

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