Consider the following sets: I. The set of even prime numbers II. \(\{x\in\mathbb{R}:x^3+1=0\}\) III. \(\{n\in\mathbb{Z}:n^2<1\}\) How many of the above are null sets?
None
Set I is \(\{2\}\) since \(2\) is the only even prime number, which is non-empty. Set II is \(\{-1\}\) since \(x^3=-1\) gives \(x=-1\), which is non-empty. Set III is \(\{0\}\) since only \(n=0\) among integers satisfies \(n^2<1\), which is non-empty. So none of the three sets is a null set.
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