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