(a) Let E be an intermediate field of the extension K ⊂ F and assume that E = K(u₁, ... , u_r) where the u_i, are (some of the) roots of ∫ ϵ K[x]. Then F is a splitting field of ∫ over K if and only if F is a splitting field of ∫ over E.

(b) Extend part (a) to splitting fields of arbitrary sets of polynomials.