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Which of the following statements is true regarding the closure of a subset $S$ of the real numbers?

Select ALL that apply.

$\overline{S}=S' \cup S$ where $S'$ is the set of limit points of $S$.

The closure of $S$ is the smallest closed set that contains $S$.

The closure of a dense subset of $\mathbb{R}$ is all of $\mathbb{R}$.

The closure of $S$ is equal to the intersection of all closed sets that contain $S$.