Mark each of the following true or false. ___ a. For all , E, there

Mark each of the following true or false. 

___ a. For all α, β ∈ E, there is always an automorphism of E mapping α onto β. 

___ b. For α, β algebraic over a field F, there is always an isomorphism of F(α) onto F(β). 

___ c. For α, β algebraic and conjugate over a field F, there is always an isomorphism of F(α) onto F(β). 

___ d. Every automorphism of every field E leaves fixed every element of the prime subfield of E. 

___ e. Every automorphism of every field E leaves fixed an infinite number of elements of E. 

___ f. Every automorphism of every field E leaves fixed at least two elements of E. 

___ g. Every automorphism of every field E of characteristic 0 leaves fixed an infinite number of elements of E. 

___ h. All automorphisms of a field E form a group under function composition. 

___ i. The set of all elements of a field E left fixed by a single automorphism of E forms a subfield of E. 

__ j. For fields F ≤ E ≤ K, G(K/E) ≤ G(K/F).