I am studying economics and I frequently encounter Binary Relations. But without any good knowledge of it, I get confused.

Here is some background, if it's helpful:

I know calculus(single and multi-variable). I have taken semester-long rigorous(definition-theorem-proof style) courses in optimization theory, linear algebra, probability theory and statistics. But, I am not very good at writing proofs myself.

I will be obliged if I will get some good text teaching me binary relations as google does not help me.


As required in comments, I add pages from a microeconomics text. Here is preface requiring a course in abstract algebra that focuses mainly on binary relations. here is first chapter of that book which uses binary relations. I hope these links will be helpful. I feel handicapped while doing exercises with binary relations. So please suggest me what shall I do.

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    $\begingroup$ I'm not sure there's a lot to be said about binary relations, per se: without more structure they are probably not very interesting. Maybe you could give some more details about the kind of things you want to know. $\endgroup$ Sep 16, 2014 at 3:48
  • $\begingroup$ @NateEldredge I do not know this will help or not: We usually use binary relations to describe preference ordering. $\endgroup$
    – Silent
    Sep 16, 2014 at 3:50
  • $\begingroup$ The general subject is called Graph Theory, a huge field. But without knowing what it is you have difficulty with, I doubt one can give useful advice. $\endgroup$ Sep 16, 2014 at 3:50
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    $\begingroup$ To be frank, what you need to add is not your personal background, but an example of the type of binary relations which you encounter during your study of economics. It suffice if you have an excerpt from a book or paper which is causing you difficulties, or perhaps a reference to where one can find such an example. From your previous comment it may be that some books on order theory may be useful, but it could also be that more generally looking at graph theory (in particular those of directed graphs) is what you need. We can't tell without more info. $\endgroup$ Sep 17, 2014 at 12:27
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    $\begingroup$ The preface does not require an abstract algebra course that focuses mainly on binary relations but the binary relations material contained in the first weeks of an undergraduate abstract algebra course. $\endgroup$
    – miracle173
    Sep 21, 2014 at 4:30

2 Answers 2


Based on the text you have provided, I'm not sure there is a book that does what you want. In particular, except the formal definition of a relation (which you don't really need), no particularly advanced knowledge is assumed. By that I mean:

  • either the definitions are provided by the text, or
  • they are easily found on Wikipedia and understanding them does not require a lot of mental aerobics.

If you insist on a book, you should be able to find this material in the intro chapter of any "Abstract Algebra" textbook, or in some section of most textbooks on "Discrete Mathematics".

Strictly speaking, it looks like your subject of interest is elementary order theory, but a book on order theory is probably more expensive than the other options and you will almost surely only use the first couple pages of it anyway.

  • $\begingroup$ Please let me know that if this is this book an order thery book? And thank you so much for so good answer. $\endgroup$
    – Silent
    Sep 21, 2014 at 10:34
  • $\begingroup$ It is a book about lattice theory, which is a subfield of order theory. It is certainly broad enough to contain what you are looking for. But as I said in my answer, I suspect you will really only be interested in pages 1 and 2 (and possibly 3, which has some good examples). $\endgroup$ Sep 22, 2014 at 1:24

This might be more advanced then you want, but a possibility is the book "Theory of Relations" by Roland Fraisse. As he says (roughly) the theory of relations isn't really the same as graph theory because in graph theory, you care more about which vertices are connected. In more abstract relation theory, the situation is more symmetric, with the two options (the relation holding or not) are on more equal footing.

  • $\begingroup$ Looks like an interesting book, +1, though I agree that it's probably not what's needed here. $\endgroup$ Sep 21, 2014 at 4:43

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