If A and B are two sets them AU (A $$\cap$$ B) will be equal to

This problem is a direct application of the Absorption Law in set theory, which states that $$A \cup (A \cap B) = A$$. This happens because the intersection $$A \cap B$$ represents only the elements common to both sets, making it a subset of $$A$$; therefore, when you take the union of $$A$$ with a part of itself, the result remains the original set $$A$$. Essentially, since every element in $$A \cap B$$ is already contained within $$A$$, adding them to $$A$$ doesn't introduce any new elements.