Simplify a set (A ∪ B)\(A \ (A ∩ B)) I'm trying to simplify a set and I'm stuck.
The set is: $(A \cup B) \setminus (A \setminus (A \cap B))$.

If someone can help with some instructions and explanations it would be great!
If $x \in (A \cup B) \setminus (A \setminus (A \cap B))$, then $(x \in A$ or $x \in B)$ and ($x \not \in A$ and $(x \in A$ and $x \in B$)).
Since $x \in A$, $x \not \in A$ is a contradiction, it must be that $x \in B$, meaning that the expression simplifies into $B$.
You could also draw Venn diagrams to get a visual as to what's actually happening.
Since this is a simple set expression involving two sets, we can check it by just using $A=\{1,3\}$ and $B=\{2,3\}$ (see here for details).

Thus we have

\begin{align}
(A\cup B)\setminus(A\setminus(A\cap B))
&amp;= (\{1,3\}\cup\{2,3\})\setminus(\{1,3\}\setminus(\{1,3\}\cap\{2,3\}))\\
&amp;= \{1,2,3\}\setminus(\{1,3\}\setminus\{3\})\\
&amp;= \{1,2,3\}\setminus\{1\}\\
&amp;= \{2,3\} = B
\end{align}

Therefore the set expression simplifies to $B$.