1. The problem asks to find the union of two sets: $A \cup B$ and $B \cup A$.\n\n2. Recall the definition of union of sets: $X \cup Y$ is the set containing all elements that are in $X$, or in $Y$, or in both.\n\n3. The union operation is commutative, meaning $A \cup B = B \cup A$.\n\n4. Therefore, $A \cup B$ and $B \cup A$ represent the same set.\n\n5. Hence, $A \cup B = B \cup A$.