Question

give an example of subsets x and y of R such that all the following conditions are satisfied:[1] x and yare not open [2]x intersect y is equal to empty set[3]x union y is open

Answer 1

Isn't that impossible, since if x=[a,b] and y=[c,d] where b<c, then xUy=[a,b]U[c,d] which is closed?