(related to Proposition: Sets are Subsets of Their Union)
- Let $A$ and $B$ be sets.
- We will prove $A\subseteq A\cup B$. The proof for $B\subseteq A\cup B$ is similar.
- Since $x\in A\cup B$ for all $x\in A$, then by definition of subset $A\subseteq A\cup B$.
- Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016