Consider $A$ = {$w, x, y, z$}. Determine:
(a) the number of possible relations on A, i.e., subsets of A×A
(b) the number of relations on A that are reflexive and symmetric.
(c) the number of relations on $A$ that are antisymmetric (consider the number of choices for a pair of element, say $(w, x)$ and $(x, w)$.
My Solutions: I was only able to solve the first part. Don't know how to solve the second or third part. (Answer (a) = $2^{16}$)
Hint:
Think every relation as a binary square matrix of size 4 whose rows and columns are marked with characters $a,b,c,d$. If $a$-th row and $c$-th column is marked 1 then $(a,b) \in R$ otherwise not. Try to observe the properties of such a matrix if $R$ is reflexive, symmetric or antisymmetric .