\begin{tabular}{l} Consider the following set of real numbers: \\ \( \left\{\pi,-\sqrt{3},-0.5,0, \frac{1}{7}, \sqrt{5}, \sqrt{9}, 3 . \overline{3}\right\} \) \\ Which of the following contains ALL of the irrational numbers in the set? \\ \( \begin{array}{l}\pi,-\sqrt{3}, \sqrt{5}, \sqrt{9} \\ \\ \pi,-\sqrt{3}, \sqrt{5} \\ \\ -\sqrt{3}, \sqrt{5}, \sqrt{9}, 3 . \overline{3}\end{array} \) \\ \( \begin{array}{l}\pi\end{array} \) \\ \( \begin{array}{l}\pi\end{array} \) \\ \hline\end{tabular}

To determine which option contains **all the irrational numbers** from the given set: \[ \left\{\pi, -\sqrt{3}, -0.5, 0, \frac{1}{7}, \sqrt{5}, \sqrt{9}, 3.\overline{3}\right\} \] **Identify the Irrational Numbers:** 1. **\(\pi\)**: Irrational. 2. **\(-\sqrt{3}\)**: Irrational. 3. **\(-0.5\)**: Rational. 4. **\(0\)**: Rational. 5. **\(\frac{1}{7}\)**: Rational. 6. **\(\sqrt{5}\)**: Irrational. 7. **\(\sqrt{9} = 3\)**: Rational. 8. **\(3.\overline{3} = \frac{10}{3}\)**: Rational. From this, the irrational numbers in the set are: \[ \pi, -\sqrt{3}, \sqrt{5} \] **Reviewing the Options:** 1. **{\(\pi, -\sqrt{3}, \sqrt{5}, \sqrt{9}\)}**: Includes \(\sqrt{9}\) (rational) — **Incorrect**. 2. **{\(\pi, -\sqrt{3}, \sqrt{5}\)}**: **All irrational numbers** — **Correct**. 3. **{\(-\sqrt{3}, \sqrt{5}, \sqrt{9}, 3.\overline{3}\)}**: Includes \(\sqrt{9}\) and \(3.\overline{3}\) (both rational) — **Incorrect**. 4. **{\(\pi\)}**: Missing \(-\sqrt{3}\) and \(\sqrt{5}\) — **Incorrect**. **Conclusion:** The correct option that contains **all the irrational numbers** from the set is: \[ \boxed{\left\{\pi,\, -\sqrt{3},\, \sqrt{5}\right\}} \]