Mark each of the following true or false. 

___ a. Every permutation is a cycle. 

___ b. Every cycle is a permutation.  

___ c. The definition of even and odd permutations could have been given equally well before Theorem 9.15. 

___ d. Every nontrivial subgroup H of S₉ containing some odd permutation contains a transposition. 

___ e. A₅ has 120 elements. 

___ f. S_n is not cyclic for any n ≥ 1. 

___ g. A₃ is a commutative group. 

___ h. S₇ is isomorphic to the subgroup of all those elements of S₈ that leave the number 8 fixed. 

___ i. S₇ is isomorphic to the subgroup of all those elements of S₈ that leave the number 5 fixed. 

___ j. The odd permutations in S₈ form a subgroup of S₈.