is it good to use two Springer Discrete Maths books for math major? Discrete Mathematics by Laszlo Lovasz, Jozsef Pelikan , Katalin L. Vesztergombi
ISBN-10: 0387955852 
A First Course in Discrete Mathematics (Springer Undergraduate Mathematics Series)
ISBN-10: 9781852332365 
are these two books suitable as Discrete Maths introductory course for undergraduate Math major?
 A: There are a number of competing criteria: max number of books, min cost (which may involve owning some books already), max depth of coverage, max breadth of coverage, max quality of writing for your level of expertise (this one is complex),... all with varying degrees of dependence.
Rosen (the discrete math text) is growing by committee in the classic commercial math text book style (adding more and more sections and history and examples and subareas) in order to be -the- text book, so that you wouldn't need any others. I personally feel this is part of the textbook publisher thrashing scheme to pull money out of students. The book may be good and constantly getting 'better', but has that general 'bloating' feel to it.
I think you can decide for yourself on a first pass the coverage of the two cheaper books against Rosen (or between any two adversarial choices) by comparing their table of contents (Rosen's is not on Amazon but directly through the publisher mhhe.com). I have used Rosen and like it for readability/I have heard that students don't care for it; I have never used Anderson or Lovasz (Lovasz's advanced books are excellent). Rosen seems geared towards CS; both Anderson and Lovasz touch on finite fields/designs which Rosen ignores altogether (but Anderson spends 1/4 of his text on it).
A: It doesn't really matter what you use, up to a certain extent.  If you use 2 different discrete math books and also several other books on other subjects, you will learn a lot.  In fact, if you use separate books for the various topics, you'll probably learn more than you would by reading Rosen's book because a textbook on a subject will have a lot more in it than a chapter of another textbook.  But, it'll also take you longer because you'll have more to read that way.
I know nothing about Rosen's discrete math book, but I have read his number theory book, well 2/3rds of it.  It also is very long and you don't need to know every detail in his book.  And you'd still learn a lot of number theory if you picked up George Andrews' "Number Theory" which is only about 250 pages.  The fact that George wrote a book on it shows that he thinks what is in his book is a good start for anyone wanting to know number theory, and that it contains all the most important things, in his opinion.  Rosen's book has all the most important stuff and a lot more stuff as well.
