Question: Suppose that E R and that C is a subset of E. a) Prove that if E is closed, then C is relatively closed

Suppose that E ⊂ R" and that C is a subset of E.
a) Prove that if E is closed, then C is relatively closed in E if and only if C is (plain old vanilla) closed (in the usual sense).
b) Prove that C is relatively closed in E if and only if E\C is relatively open in E.

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