Which set contains an irrational number? \( \begin{array}{l}\{0,1,2,3,-1\} \\ \{0.17, \sqrt{3}, 2 . \overline{5}, \sqrt{4}\} \\ \left\{\frac{1}{2}, \frac{3}{5}, \frac{15}{3},-\frac{7}{2}, 1 \frac{5}{6}\right\} \\ \{\sqrt{100}, 0.125125125,-1.0888\}\end{array} \)

To determine which set contains an irrational number, let's analyze each set individually. 1. **Set A: \(\{0, 1, 2, 3, -1\}\)** - All elements are integers, which are rational numbers. 2. **Set B: \(\{0.17, \sqrt{3}, 2.\overline{5}, \sqrt{4}\}\)** - **0.17** is a rational number (\( \frac{17}{100} \)). - **\(\sqrt{3}\)** is an **irrational** number. - **\(2.\overline{5}\)** (which represents \(2.5555...\)) is a rational number (\(\frac{25}{9}\)). - **\(\sqrt{4}\)** is a rational number (\(2\)). 3. **Set C: \(\left\{\frac{1}{2}, \frac{3}{5}, \frac{15}{3}, -\frac{7}{2}, 1 \frac{5}{6}\right\}\)** - All elements are fractions or integers, which are rational numbers. 4. **Set D: \(\{\sqrt{100}, 0.125125125, -1.0888\}\)** - **\(\sqrt{100}\)** is a rational number (\(10\)). - **0.125125125...** is a repeating decimal, which is rational (\(\frac{125}{999}\)). - **-1.0888...** is also a repeating decimal, which is rational. **Conclusion:** Only **Set B** contains an irrational number, which is \(\sqrt{3}\). **Answer:** \(\{0.17, \sqrt{3}, 2.\overline{5}, \sqrt{4}\}\)