1. **Problem:** Determine if the statement "The solution set for $x^2 = 81$ is \{9\}" is true or false. 2. **Formula and rules:** To solve $x^2 = 81$, we use the property that if $x^2 = a$, then $x = \pm \sqrt{a}$. 3. **Solve the equation:** $$x^2 = 81$$ Taking the square root of both sides: $$x = \pm \sqrt{81}$$ $$x = \pm 9$$ 4. **Interpretation:** The solutions are $x = 9$ and $x = -9$, so the solution set is \{9, -9\}. 5. **Conclusion:** The statement that the solution set is \{9\} only is **false** because it excludes $-9$. **Final answer:** False