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## Homework Statement

Find subsets E[tex]\subset[/tex]S1[tex]\subset[/tex]S2[tex]\subset[/tex]S3[tex]\subset[/tex]Q such that E has a least upper bound in S1, but does not have any least upper bound in S2, yet does have a least upper bound in S3.

## Homework Equations

## The Attempt at a Solution

I got totally stuck with it. If a[tex]\in[/tex]S1 is the least upper bound of E, does that mean a is also in S2 and hence a least upper bound of E in S2?

On the other hand, if E has a least upper bound b in Q, is b unique? So in any subset S of Q, just check if b is in S to see if E has a least upper bound in S?

Thanks a lot