Empty Set and Set form Algebra of Sets
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Let $S$ be any non-empty set.
From Set Union is Idempotent:
- $S \cup S = S$
- $\O \cup \O = \O$
Then from Union with Empty Set:
- $S \cup \O = S$
- $\relcomp S \O = S$
- $\relcomp S S = \O$
Hence the result, by definition of algebra of sets.