| context | $X,Y$ … set |
| definiendum | $ x\in X \cup Y $ |
| postulate | $ x\in X\lor x\in Y $ |
The 2-ary set construction $ X \cup Y $ is commutative and idempotent.
Notice that $ X \cup \emptyset = X$.
The union and intersection are associative and distributive with respect to another.
Wikipedia: Union