Good book for self-studying Binary Relations

Question

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.

Edit:

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.

Answer 1

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.

Answer 2

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.