Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question
    
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
2  
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
show 1 more comment

1 Answer 1

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

share|improve this answer
    
Thank you so much. Why did I not see that... –  kshong Mar 19 '13 at 8:33
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.