Part CCSIR NET December 2024separability-is-free-in-all-four-settings

Separability is free in all four settings

Which of the following statements are true?

A.If K is the splitting field of a non-constant polynomial over $Q$ , then K is Galois over $Q$ .✓
B.If K is a normal extension of $Q$ , then K is Galois over $Q$ .✓
C.If K is the set of all the roots of the polynomial $x^{121} - x$ in an algebraic closure of 𝔽 $_{11}$ , then K is Galois over 𝔽 $_{11}$ , where 𝔽 $_{11}$ is the field with 11 elements.✓
D.If $K = Q (2^{(} 1/13), ζ_{13})$ , where $ζ_{13}$ is a primitive 13th root of unity in $C$ , then K is Galois over $Q$ .✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

50 are analysed free — try those first.

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