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Let E/F be an algebraic extension. Let K and L be intermediate fields (i.e. F ⊆...

Let E/F be an algebraic extension. Let K and L be intermediate fields (i.e. F ⊆ K ⊆ E and F ⊆ L ⊆ E).

(i) Prove that if the extension K/F is separable then the extension KL/L is separable.

(ii) Prove that if the extension K/F is normal then the extension KL/L is normal.

Note: To make things easier for you, you can assume that E/F is finite (hence all extensions are finite),

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