北京邮电大学 离散数学下 群论 作业错题讲解(2)

北京邮电大学离散数学群论作业详解

群论9.1-9.2 （1）20,28 @323-324

1. ≤is reflexive

Since a= a*a, a≤a for all a in A.

2. ≤is antisymmetric

suppose that a≤b and b≤a.

Then, b = a*b= b*a= a, so a= b.

3. ≤is transitive

If a≤b and b≤c, then c= b*c= (a*b)*c= a*(b*c)= a*c, so a≤c.