Mark each of the following true or false. 

___ a. The associative law holds in every group.

___ b. There may be a group in which the cancellation law fails.

 ___ c. Every group is a subgroup of itself. 

___ d. Every group has exactly two improper subgroups. 

___ e. In every cyclic group, every element is a generator. 

___ f. A cyclic group has a unique generator. 

___ g. Every set of numbers that is a group under addition is also a group under multiplication. 

___ h. A subgroup may be defined as a subset of a group. 

___ i. Z₄ is a cyclic group. 

___ j. Every subset of every group is a subgroup under the induced operation.