Is this proof of $A \cup (B - (A \cap B)) \subseteq A \cup B$

Question

My try:

Suppose $x \in A \cup (B - (A \cap B))$.

If $x \in A$, then $x \in A \cup B$.

If $x \in B - (A \cap B)$, then $x \in B$ and $x \notin A \cap B$.

Specificaly, $x \in B$. Hence $x \in A \cup B$.

Then, by subset definition, we have $A \cup (B - (A \cap B)) \subseteq A \cup B$.

Answer 1

Yes your proof is correct. You have showed the steps required for the solution.