Intersection of two equivalence relations is also a equivalce relation?? if yes, How??

Use the fact that R and S are EQUIVALENCE relations on THE SAME set, and hence both must be reflexive, symmetric, and transitive on that set.Then use the definition of set intersection: R∩S is the set of all pairs of elements in the set such that (x,y)∈R AND (x,y)∈S or, put differently, (x,y)∈R∩S⟺(x,y)∈R and (x,y)∈S.

Try to figure out what elements must necessarily be in R∩S and check to see that they must then be in both R and S.