Case 1: Scheme R has attributes A, B, C, and D. Tuple t over scheme R has values 1, 2, 3, and 4, respectively. Scheme S has attributes C, D, E, and F. Tuple u over scheme S has values 3, 4, 5, and 6, respectively. The intersection of schemes R and S contains attributes C and D. The values of C and D are the same in both tuples t and u. The result scheme, R union S, contains attributes A, B, C, D, E, and F. The result tuple, paste (t, u) over the scheme R union S, contains the attributes 1, 2, 3, 4, 5, and 6, respectively.

Case 2: Scheme R has attributes A, B, C, and D. Tuple t over scheme R has values 1, 2, 3, and 4, respectively. Scheme S has attributes C, D, E, and F. Tuple u over scheme S has values 3, 5, 6, and 7, respectively. The intersection of schemes R and S contains attributes C and D. The values of C are the same in both tuples t and u, but the values of D are different. There is no tuple that results from the operation paste (t, u).

Case 3: Scheme R has attributes A, B, C, and D. Tuple t over scheme R has values 1, 2, 3, and 4, respectively. Scheme S has attributes E, F, G, and H. Tuple u over scheme S has values 5, 6, 7, and 8, respectively. The intersection of schemes R and S is null. The result scheme, R union S, contains attributes A, B, C, D, E, F, G, and H. The result tuple, paste (t, u) over the scheme R union S, contains the attributes 1, 2, 3, 4, 5, 6, 7, and 8, respectively.