How do I prove that the induction schemes namely CVI, LNP, SI are Equivalent?

Answer 1

I am not sure what all of your abreviations are for (sometimes the words vary from book to book, so it is best to write them out). The proofs that they are equivalent are in many different books. I know that the proof that strong induction is equivalent to weak induction is in Abstract Algebra by Dummit and Foote as well as Contemporary Abstract Algebra by Joseph A. Gallian. You can also find the proofs in number theory books and discrete math books.