Set X = {1, 2, ..., n} where n>200
Can I find relation R such that there are n-1 pairs? How about n, n+1, n+2, n+3 and n(n-1) pairs?
If not, how would I prove that there can not exist equivalence relation R such that the number of pairs is one of the above quantities without using contradiction or contrapositive proof?
I've thought about a relation where (x-y)=1 for n-1, but I don't believe its reflexive so its not an equivalence relation.