Let A={v, w, x, y, z}
Determine the number of relations on A that are reflexive and symmetric but not transitive.
Attempt:
There are $2^{25}$ total relations. For transitivity, we are taking pairs like (a, a) (b, b) for granted and there are n of them, then there are $2^{25-5}=2^{20}$ relations which are transitive.
For symmetric, we have to pick subsets of 2 of the set A because then the partition {a,b} will give the relation both (a,b) and (b,a). There are $C(5,2)$ subsets of 2. Then there are $2^{C(5,2)}$ relations which are symmetric.
I'm stuck at transitivity. What I'm gonna do here?