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Problem 69 (Showing The Existence of a Field Extension Generated by a subset)
Suppose that $E$ is an extension field of the field $F$. Let $S$ be a subset of $E$.
- Prove that there is a subfield of $E$ that contains both $F$ and $S$.
- Prove that the intersection of all subfields of $E$ that contain both $F$ and $S$ is a subfield of $E$.
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