1. **State the problem:** Evaluate $\{x \mid x=4\}$. 2. **Use the definition of set-builder notation:** This means “the set of all $x$ such that $x=4$.” 3. **Substitute the value:** Since the only value that satisfies the condition is $x=4$, the set contains just one element. 4. **Final answer:** $\{4\}$