There are pairs in that table so
Therefore there are off diagonal pairs.
Any reflexive relation on must contain .
So any reflexive relation is the union of with any subset of off diagonal pairs.
How many of those are there?
Any symmetric relation on , , has the property that .
There are pairs either on the diagonal or above it.
Any subset of those pairs corresponds to a symmetric relation.
Just take that subset and unite it with its inverse.
How many are there?