# Do not understand what this question is asking… or the notation, Discrete Structures/Relations

Let X = {1,2,....,10} Define a relation R on X x X by (a,b)R(c,d) if a + d = b + c

I lose track of what it is asking on the part italicized. I have a similar question that ends in ad = bc as well with everything prior being similar.

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I still do not understand, maybe someone could show me how it works with a different X, maybe X = { 23, 24, 25, ... 33} so that I can see how it works. I want to understand the concept fully, then I can apply it to the original X set. – Matt Apr 25 '13 at 3:37

This relation is on pairs of integers. $(1,2)$ is related to $(3,4)$ because $1+4=2+3$. $(1,2)$ is not related to $(5,4)$ because $1+4\neq 2+5$. Hence, some pairs are related to other pairs. What you do with this information depends on what comes next.
$(1,2)$ is related to $(1,2)$ because $1+2=2+1$. Also $(1,2)$ is related to $(10,11)$ because $1+11=2+10$. All such combinations... – vadim123 Apr 25 '13 at 3:18
You're right, any $(a,a)$ is related to any $(b,b)$, but $(1,2)$ isn't related to any $(a,a)$. You're not missing anything. It's not like if two elements aren't related you're doing something wrong. Some pairs are related to other pairs, and some aren't. – vadim123 Apr 25 '13 at 3:37
In words, what this is saying is that if you want to see if any two pairs of numbers in $X$ are related such as $(a,b)$ and $(c,d)$, for any $a,b,c,d \in X$, you find $a+d$ and see if it equates to $b+c$ if it does then the two are considered related by the definition of relation given.