Regarding definition of Borel Sets is $ \sigma $ ring of sets

Question

I am self studying Measure and Integration from book Hari Bercovici, Arlen Brown and I need help in proving definition that Borel sets is a $ \sigma $ ring of sets . Authors defines A ring of sets as follows - A collection C of subsets of a set X is called Ring if - 1. It is closed wrt to formation of union. 2. It is closed wrt formation of differences ie if A and B belongs to C then A\ B also belongs to C. Then if some addition conditions hold then it is called $ \sigma $ ring of sets . I cannot prove 2 nd condition of ring in case of Borel sets. Definition of ring of Borel sets in X - In any metric space (X, d) , the topology G , that is, collection of all open sets in X , generates a $ \sigma $ ring of sets called ring of borel sets. So, I want to ask how does topology generates a ring ie if P and Q belongs to Collection C how to prove P\ Q also belongs to C. An example which I thought - take eucledian metric on Real line and (0, 5 and (1, 2) are open. Then (0, 5) \ (1, 2) is (0, 1] union [2, 5) is not open but it is contained into open sets but these Sets doesn't belong to C. I am really confused how to prove 2 nd condition . please help.