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Prove the First Complementarity Theorem: Suppose S is a point set. Let Sc be the complement...

Prove the First Complementarity Theorem: Suppose S is a point set. Let Sc be the complement of S.

1) S and Sc have the same boundary.

2) The interior of S is the same as the exterior of Sc.

3) The exterior of S is the same as the interior of Sc.

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