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Consider this relation; $$R = \{(1,1),(1,3),(1,4),(1,5),(2,2),(2,4),(2,3),(3,3),(3,4),(3,5),(4,4),(4,5),(5,5)\}$$

R is reflexive, transitive and antisymmetric. Therefore R is partially ordering relation. I want to draw a Hasse diagram for this relation. 2 and 5 are not related. So I placed them at same level. But 3 and 5 are related and 2 and 3 are related which makes me place 2 below 3 and 3 below 5 and in turn it shows 2 is related to 5 but it is not! . Where did I make mistake? How to place 2, 3, 5 in correct order? Any help would be greatly appreciated.

Edit: This relation is not transitive. If (2,3) and (3,5) are elements in R, then (2,5) should be! Otherwise transitive condition would fail. I couldn't see that at first place.

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  • $\begingroup$ It seems that R is not reflexive, because (5,5) does not belong to R. $\endgroup$
    – user376343
    Commented Dec 16, 2020 at 16:20
  • $\begingroup$ Deleting this question. It is not a transitive relation. $\endgroup$
    – mig001
    Commented Dec 16, 2020 at 16:33

1 Answer 1

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The relation given is neither transitive nor reflexive.

For a start it does not include $(5, 5)$.

For another thing, while $(2, 3)$ and $(3,5)$ are there, $(2, 5)$ is not.

If you were to create the reflexive closure and transitive closure, you should be able to work with it, but at the moment it is not a partial ordering.

Maybe you transcribed it wrong, and it should be $(2,5)$ instead of $(2, 3)$.

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  • $\begingroup$ (5,5) was unintentional. Corrected it! By the way second mistake is exactly what I was searching to find. Actually (2,5) was there in the actual problem. I removed it to make an hypothetical situation were an element has to be placed both on top and bottom of an element. But failed! I think transitive relation won't allow that to happen. Sorry I missed that one. Thank you. $\endgroup$
    – mig001
    Commented Dec 16, 2020 at 16:32

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