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Previous Year Question (PYQs)

What are the greatest lower bound $($GLB$)$ and the least upper bound $($LUB$)$ of the sets $A={3,9,12}$ and $B={1,2,4,5,10}$ if they exist in poset $(Z^+,/)$?




Solution

In the poset $(Z^+,/)$, the relation is based on divisibility.

Here,

$GLB=$ greatest common divisor $($GCD$)$

$LUB=$ least common multiple $($LCM$)$

For set $A={3,9,12}$:

$GLB(A)=GCD(3,9,12)=3$

$LUB(A)=LCM(3,9,12)=36$

For set $B={1,2,4,5,10}$:

$GLB(B)=GCD(1,2,4,5,10)=1$

$LUB(B)=LCM(1,2,4,5,10)=20$

So,

$A(GLB-3,\ LUB-36)$

and

$B(GLB-1,\ LUB-20)$


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