北京邮电大学 离散数学下 群论 作业错题讲解(3)

北京邮电大学离散数学群论作业详解

群论9.1-9.2 （1）28 @323-324

show a*b= a∨b, for all a and b in A

(1)a*b= a*(b*b) =(a*b)*b=b*(a*b), so b ≤a*b.

In a similar way, a*b= (a*a)*b=a*(a*b), so a≤a*b.

so a*b is a upper bound for a and b.

(2)if a≤c and b≤c.then c= a*c and c= b*c by definition. Thus c= a*(b*c)= (a*b)*c. so a*b≤c.

This shows that a*b is the leastest upper bound of a and b.

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