Please have a look at the Hasse diagram -
How come the upper bounds of {a,b,c} are e,f,j and h and lower bound is a
Why doesn't it include d and g also in its upper bound?
can anyone please clarify this?
Please have a look at the Hasse diagram -
How come the upper bounds of {a,b,c} are e,f,j and h and lower bound is a
Why doesn't it include d and g also in its upper bound?
can anyone please clarify this?
Okay, here are my questions...
1) {b,d,g} upper bounds - g and h
my question - why not only "h" why include g in it?
2) {b,d,g} least upper bound - g
my question - How come it is "g" why not "h" since h>g
3) {b,d,g} lower bounds - a and b
my question - why not only "a" why include b in it?
4) {b,d,g} greatest lower bound - b
my question - why not "a" since a<b
5) {a,c,d,f} upper bounds - f,h and j
my question - why include "f" in upper bound? Also, there is no "upward" connection between a and d.
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).
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.
3) {b,d,g} lower bounds - a and b
my question - why not only "a" why include b in it?
See 1). It is the same reason: b proceeds each element in the set.
4) {b,d,g} greatest lower bound – b my question - why not "a" since a<b
See 2). It is the same reason: b is the greatest or last upper bound.
5) {a,c,d,f} upper bounds - f,h and j
my question - why include "f" in upper bound? Also, there is no "upward" connection between a and d.
"a-b-d is an upward" connection between a and d.
There is an "upward" connection between any term in {a,c,d,f} to f [recall (f,f)]..
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!
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? In this case it is {b,d,g} so here it is "b". Is it also the greatest lower bound?