Mark each of the following true or false. 

___ a. If G₁ and G₂ are any groups, then G₁ x G₂ is always isomorphic to G₂ x G₁• 

___ b. Computation in an external direct product of groups is easy if you know how to compute in each component group. 

___ c. Groups of finite order must be used to form an external direct product. 

___ d. A group of prime order could not be the internal direct product of two proper nontrivial subgroups. 

___ e. Z₂ x Z₄ is isomorphic to Z₈. 

___ f. Z₂ x Z₄ is isomorphic to S₈ • 

___ g. Z₃ x Z₈ is isomorphic to S₄.

___ h. Every element in Z₄ x Z₈ has order 8. 

___ i. The order of Z₁₂ x Z₁₅ is 60. 

___ j. Z_m x Z_n has mn elements whether m and n are relatively prime or not.