Please check if my answer is correct and what should be add to my answer,My Ans is in the pdf ,please give me some advice

Suppose we are given a relation R on a set S. Define the relation R' as follows: R' = RU(s, S) |s ES That is to say, R' contains all the pairs in R, plus all pairs of the form (s, s). Show that R' is the reflexive closure of R. Ans: Step 1:R is contained in the R' Step 2:(s, s) ( S is contained in the R' and R' is reflexive. Step 3: We assume R' is the reflexive closure of R, So for any (X, Y) E R' , (X, Y) E R , or (X, Y) E (s, s) ES Because R is in the R' and R' is reflexive ,according to the definition of reflexive closure , R' is the reflexive closure of R