1. **Problem:** Write the set $V = \{a,e,i,o,u\}$ in set builder form. 2. **Formula and Explanation:** Set builder notation describes a set by a property that its members satisfy. For vowels, the property is "being a vowel in English alphabet." 3. **Solution:** $$V = \{ x \mid x \text{ is a vowel in English alphabet} \}$$ This means $V$ is the set of all $x$ such that $x$ is a vowel. **Final answer:** $$V = \{ x \mid x \in \{a,e,i,o,u\} \}$$