(related to Proposition: Set Union is Commutative)
- Suppose that $A$ and $B$ are any sets.
- We want to show that the set union $A\cup B$ is commutative, i.e. $A\cap B=B\cup A.$
Part 1: $A\cup B\subseteq B\cup A$
Part 2: $B\cup A\subseteq A\cup B$
- The proof is identical to Part 1 if we exchange the denotations of $A$ and $B.$
Thank you to the contributors under CC BY-SA 4.0!
- Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016