Write now, analyze later. On the Theory of Classes. They are persons. On the Theory of Relations. Relations of the 2nd order are those which hold between classes or relations of the 1st order, and so on.
R is the relation.
In the Trinity, relations do exist between the 3 persons. This seems to be a symmetrical relation. Note - do not confuse the usage of the term 'God the Father' with 'God'. Yes, the Father is God, just as the Holy Spirit is God. But the Holy Spirit is not God, the Father.