1) If $K$ is a field of characteristic zero and $[L : K]$ is an extension with $[L : K] = 2$, then $L : K$ is a Galois extension.
2) Let $K$ be a field, and let $f ∈ K[X]$ be a polynomial with degree $d$. Then $[Σ : K] = d$, where $Σ$ is any splitting field of $f$ over $K$.
3) If $L$ is a field such that $Q ⊂ L ⊂ Q(ζ)$, where $ζ$ is a primitive $n^{th}$ root of unity, then $L : Q$ is a Galois extension.
I am not sure how to go about solving these. I know that for 3), if we have any positive integer $n$ and a primitive $n^{th}$ root of unity, we get that $Q(ζ) : Q$ is a Galois extension, but I'm not sure how this extends to intermediate extensions. Apologies if these are basic questions, I am very new to Galois theory and have not been taught formally.