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.