Define a relation R on R (All Real Numbers) as follows: For all real numbers x and y mTn if and only if 3 | (m - n).
I'm not sure what the vertical bar here means. Normally it means "such as" but that doesn't make sense in this context so what does it mean? Thank you!
EDIT: So would the answer to this question be R = { (x,y) | 3 | (x - y) }?
There is no question there, and nothing that demands a solution. The text
is not an exercise, and it doesn't ask you to do anything. On the contrary, the quoted text is a definition of $R$.
(Here I'm ignoring that it seems to confuse $x$ and $y$ for $m$ and $n$; I suspect you have copy-pasted a bit too eagerly from your earlier question).
If the text appears on a homework sheet, it is not because you're expected to give a definition of $R$ in your answer (because the text on the sheet is the definition) -- it is just there to tell you what $R$ means in the text below what you quote is speaking about. (Presumably there will be some kind of question about the $R$ that was just defined).
As others have noted in comments, $3\mid (m-n)$ means the $m-n$ is an (integer) multiple of $3$.