Question 4
Among the four statements on real numbers below, how many of them are correct?
1. If \(a\lt b\lt 0\), then \(a\lt b^2\).
2. If \(0\lt a\lt b\), then \(a\lt b^2\).
3. If \(a^3\lt b^3\), then \(a\lt b\).
4. If \(a^2\lt b^2\), then \(a\lt b\).
5. If \(|a|\lt |b|\), then \(a\lt b\).
Editorial reading note: the source says “four statements” but actually displays the five statements above. Count all five displayed statements.
1. If \(a\lt b\lt 0\), then \(a\lt b^2\).
2. If \(0\lt a\lt b\), then \(a\lt b^2\).
3. If \(a^3\lt b^3\), then \(a\lt b\).
4. If \(a^2\lt b^2\), then \(a\lt b\).
5. If \(|a|\lt |b|\), then \(a\lt b\).
Editorial reading note: the source says “four statements” but actually displays the five statements above. Count all five displayed statements.