Mark each of the following true or false.
___ a. No proper algebraic extension of an infinite field of characteristic p ≠ 0 is ever a separable extension.
___ b. If F(a) is totally inseparable over F of characteristic p ≠ 0, then α^P' ∈ F for some t > 0.
___ c. For an indeterminate y, Z₅(y) is separable over Z₅(y⁵).
___ d. For an indeterminate y, Z₅(y) is separable over Z₅(y¹⁰).
___ e. For an indeterminate y, Z₅(y) is totally inseparable over Z₅(y¹⁰).
___ f. If F is a field and α is algebraic over F, then α is either separable or totally inseparable over F.
___ g. If E is an algebraic extension of a field F, then F has a separable closure in E.
___ h. If E is an algebraic extension of a field F, then E is totally inseparable over the separable closure of F in E.
___ i. If E is an algebraic extension of a field F and E is not a separable extension of F, then E is totally inseparable over the separable closure of F in E.
___ j. If α is totally inseparable over F, then α is the only zero of irr(α, F).