1. The problem is to simplify the set expression $$A \cup B \cap A$$. 2. Recall the order of operations in set theory: intersection ($\cap$) is performed before union ($\cup$). 3. So, we first evaluate $$B \cap A$$, which is the intersection of sets $B$ and $A$. 4. The intersection $B \cap A$ contains all elements that are in both $B$ and $A$. 5. Next, we take the union of $A$ with the result of $B \cap A$, i.e., $$A \cup (B \cap A)$$. 6. Since $B \cap A$ is a subset of $A$, the union of $A$ with any subset of $A$ is just $A$ itself. 7. Therefore, the simplified expression is $$A$$. Final answer: $$A$$