# Need help understanding binary relations…

Let $R$ be a relation on a set $A$. Is $R$ a partial order?

$A = \{0,1,2,3\}$

$R = \{(0,0), (1,1), (2,0), (2,2), (2,3), (3,2), (3,3)\}$

I know that it's reflexive, not anti-symmetric, and not transitive. I have the answer.

Can someone explain to me why it is not transitive?

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Is $R$ correctly written? With the pairs $(2,3)$ and $(3,2)$ in, it is definitely not ant-symmetric. –  Andreas Caranti Mar 19 '13 at 8:25
Please note the simple $\LaTeX$ formatting I did to the text of your question. –  Andreas Caranti Mar 19 '13 at 8:27
Yes, R is correctly written. I have taken it from the lecture slides. I did mention that it is not antisymmetric. –  kshong Mar 19 '13 at 8:28
Ah, ok, but then it's not a partial order. –  Andreas Caranti Mar 19 '13 at 8:30
Did you try to draw it on paper (you know, with relations written as arrows going from a point to another) ? If you did, then you should see immediately which arrow is missing. –  Djaian Mar 19 '13 at 8:41

## 1 Answer

It's not transitive because $3$ relates to $2$, $2$ relates to $0$, but $3$ does not relate to $0$.

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Thank you so much. Why did I not see that... –  kshong Mar 19 '13 at 8:33