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I am stuck with a question. It is stated below.

Let $R$ be a relation defined on the set of integers $\mathbb Z$ by the rule $aRb \iff |a-b|\leq 2$. Write the relation $R$ as a set.

Now there can be too many sets that satisfy this relation. How do I write the set $R$ representing the relation?

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1  
Where did you see this question? It's a bit gnarly to make sense of your expression as it stands... –  J. M. Jul 31 '11 at 15:37
    
What's the question? What is $A$ and $Z$? –  Jack Jul 31 '11 at 15:42
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OP can correct me if I'm wrong, but I believe he or she wishes to set up a relation on the set $\mathbb{Z}$ defined by $a\sim b$ whenever $|a-b|\le 2$. My answer is based on that interpretation. –  anon Jul 31 '11 at 15:47
    
I think the $A$ is supposed to mean the domain of $R$, and of course, the relation satisfies the rule $aRb \iff |a-b| \leq 2$. I will edit the question assuming this. Anyone knows what the tabular notation is? @fahad Please try to state your question more clearly, and using well-defined notation. Also typeset the math in latex. –  Srivatsan Jul 31 '11 at 15:47

1 Answer 1

up vote 4 down vote accepted

Given an integer $a$, the only integers $b$ which satisfy $|a-b|\le 2$ are $b=a-2,a-1,a,a+1,a+2$.

Thus the relation can be represented by the set $\{(n,n+k): n\in\mathbb{Z}, k\in\{-2,-1,0,1,2\}\}\subset\mathbb{Z}^2$.

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