# Math Help - relations

1. ## relations

Let B={1,2,3.....m), let R be a relation on B and its antisymmetric

a) What is the biggest number of ordered pairs that can be in R?

b)How many antisymmetric relations on A have the size found in a) ??

2. (a)Since the matrix representation M of R can be a upper triangle matrix, it has the bigggest oder $\frac{n(n+1)}{2}$.
(b)Since the element in the diagonal of M should be 1, Thus there are $2^{\frac{n(n-1)}{2}}$ distinct antisymmetric relations on B having the size found in (a)

3. The same problem was also considered here. If you have difficulties, I suggest starting with writing some examples of such relations with the maximum number of pairs for small $m$.