Mark each of the following true or false. 

___ a. Every boundary is a cycle. 

___ b. Every cycle is a boundary. 

___ c. C_n(X) is always a free abelian group.

___ d. B_n(X) is always a free abelian group. 

___ e. Z_n(X) is always a free abelian group. 

___ f. H_n(X) is always abelian. 

___ g. The boundary of a 3-simplex is a 2-simplex. 

___ h. The boundary of a 2-simplex is a 1-chain. 

___ i. The boundary of a 3-cycle is a 2-chain. 

___ j. If Z_n(X) = B_n(X), then H_n(X) is the trivial group of one element.