1. **State the problem:** Write the set $E = \{2, 4, 6, 8, 10\}$ in rule form. 2. **Formula and explanation:** Rule form expresses a set by a property that its members satisfy, usually written as $\{x \mid \text{property of } x\}$. 3. **Identify the pattern:** The elements are even numbers starting from 2 up to 10. 4. **Write the rule:** Each element is an even number $x$ such that $x$ is between 2 and 10 inclusive. 5. **Express in rule form:** $$E = \{x \mid x = 2n, n \in \mathbb{Z}, 1 \leq n \leq 5\}$$ or equivalently, $$E = \{x \mid x \text{ is even and } 2 \leq x \leq 10\}$$ This means $E$ contains all $x$ such that $x$ is an even integer between 2 and 10 inclusive. **Final answer:** $$E = \{x \mid x = 2n, n \in \mathbb{Z}, 1 \leq n \leq 5\}$$