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

Question

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.

Thanks for your help!

Answer 1

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.

Answer 2

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.