Simplifying a set theory expression

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I'm learning the different laws used to simplify set theory expressions and I'm stuck at a more difficult task. I want to simplify the following expression:

$$\begin{align} (A \cup B) \setminus (A \setminus (A \cap B)) & = (A \cup B) \cap (A \setminus (A \cap B))' \\ & = (A \cup B) \cap (A \cap (A \cap B)')' \\ & = (A \cup B) \cap (A' \cup (A \cap B)) \\ & = ? \end{align} $$

What I wonder is how I proceed from here; I feel stuck.

Thanks in advance; and sorry I could not get the MathJaX to work, I'll learn it until next time.

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1 Answer

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$$(A \cup B) \cap (A' \cup (A \cap B))$$ $$(A \cup B) \cap ((A' \cup A) \cap (A' \cup B))$$ $$(A \cup B) \cap (\text{"All"} \cap (A' \cup B))$$ $$(A \cup B) \cap (A' \cup B)$$ $$(A \cup A') \cap B$$ $$\text{"All"} \cap B$$ $$B$$

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