# Thread: Hasse Diagram - lower upper bound

1. {a,c,d,f} upper bounds - f,h and j
my question - why include "f" in upper bound?

2. Originally Posted by robocop_911
{a,c,d,f} upper bounds - f,h and j
my question - why include "f" in upper bound?
try understanding the definition like what plato said..
post the definition you have and point us what you dont understand on the statement..

3. Originally Posted by robocop_911
1) {b,d,g} upper bounds - g and h
my question - why not only "h" why include g in it?
Because both succeed every term in {b,d,g}. Don’t forget that partial orders are reflexive, therefore (g,g).
Then how come upper bounds of {a,b,c} is e,f,j and h and not something like c,e,f,j,h? (c,c) (b,b) that's also reflexive!
because, they are not connected to all of a,b and c..
Originally Posted by robocop_911
2) {b,d,g} least upper bound - g
my question - How come it is "g" why not "h" since h>g
Because there is only one LUB for any given set and g is the first or least.

So least upper bound should be from the set given only right?
not all the time..
Originally Posted by robocop_911
In this case it is {b,d,g} so here it is "b". Is it also the greatest lower bound?
yes, you are right..

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# upper bound and lower bound in discrete mathematics

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