# Poset troubles

• Sep 5th 2010, 03:13 AM
primeimplicant
Poset troubles
Hello ppl :-)

A={3,5,9,15,24,45} . Also R={(x,y) | x divides y} . Proove that
1) R is partial ordered

2) Hasse diagramm for R

3) Upper bounds of {3,5} , Lower bounds for {15,45}

-------

for 1) i have to show that R is reflexive, antisymmetric, and transitive

not sure how to show it for this particular problem though.

2) xy
/ \
x y
\ /
0

3) No idea =/
• Sep 5th 2010, 09:56 AM
emakarov
Quote:

for 1) i have to show that R is reflexive, antisymmetric, and transitive

not sure how to show it for this particular problem though.
Start by writing the definition: what it means for R to be reflexive. Substitute the definition of R into that expression.

Quote:

2) xy
/ \
x y
\ /
0
A Hasse diagram is a graph where vertices are elements of the partially ordered set, i.e., A. Zero is not a member of A and neither are x and y.

Quote:

3) Upper bounds of {3,5} , Lower bounds for {15,45}
Again, write the definition, what it means for a number x to be an upper bound of 3 and 5 and substitute the definition of R there.