Set Difference is Disjoint with Reverse

Theorem

 * $$\left({S \backslash T}\right) \cap \left({T \backslash S}\right) = \varnothing$$

Proof
We assume that $$S, T \subseteq \mathbb U$$ where $$\mathbb U$$ is the universe.

Then we can use the definition of Set Difference as Intersection with Complement.

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