Mark each of the following true or false.

_______ a. Every finite extension of every field F is separable over F.

_______ b. Every finite extension of every finite field F is separable over F.

_______ c. Every field of characteristic 0 is perfect.

_______ d. Every polynomial of degree n over every field F always has n distinct zeros in F̅.

_______ e. Every polynomial of degree n over every perfect field F always has n distinct zeros in F̅.

_______ f. Every irreducible polynomial of degree n over every perfect field F always has n distinct zeros in F̅.

_______ g. Every algebraically closed field is perfect.

_______ h. Every field F has an algebraic extension E that is perfect.

_______ i. If E is a finite separable splitting field extension of F, then |G(E/F)| = [E : F].

_______ j. If E is a finite splitting field extension of F, then |G(E/F)| divides [E : F].