1. **Problem:** Find a set of three rational numbers between 1 and 2. 2. **Understanding Rational Numbers:** Rational numbers are numbers that can be expressed as a fraction $\frac{a}{b}$ where $a$ and $b$ are integers and $b \neq 0$. 3. **Choosing Rational Numbers Between 1 and 2:** - We need three numbers $x$ such that $1 < x < 2$. - Examples include fractions like $\frac{3}{2}$, $\frac{5}{4}$, and $\frac{7}{5}$. 4. **Expressing the Set:** - The set can be written as $\{\frac{3}{2}, \frac{5}{4}, \frac{7}{5}\}$. 5. **Explanation:** - $\frac{3}{2} = 1.5$, $\frac{5}{4} = 1.25$, and $\frac{7}{5} = 1.4$ are all rational numbers strictly between 1 and 2. **Final answer:** $$\{\frac{3}{2}, \frac{5}{4}, \frac{7}{5}\}$$