So I am to determine the number of both symmetric and reflexive relations on an n-element set. I've read various explanations (yes, Number of relations that are both symmetric and reflexive too) but I still don't quite get it.
If the relations are to be both symmetric and reflexive, why isn't the answer the same as for the reflexive? I mean - when we have some 25-element set, represent it as 5x5 grid, no other points can be symmetric and reflexive at the same time than the diagonal from (1,1) to (5,5). We can choose many symmetric ones apart from those too, but neither will be reflexive.
What do I not understand?