Consider relation R(A,B,C,D,E) with multivalued dependencies:A ↠ B, B ↠ DSuppose R contains the tuples (0,1,2,3,4) and (0,5,6,7,8). Which of the following tuples must also be in R?

The multivalued dependencies A ↠ B and B ↠ D mean that if two tuples of R agree on attribute A, they must agree on attribute B, and if two tuples agree on attribute B, they must agree on attribute D.

Given the tuples (0,1,2,3,4) and (0,5,6,7,8), we can see that they agree on attribute A (since both have 0 for A). Therefore, by the multivalued dependency A ↠ B, they must agree on attribute B. However, they do not (since the first tuple has 1 for B and the second has 5).

Therefore, we can infer that the following tuples must also be in R:

(0,1,2,7,8) and (0,5,6,3,4)

These tuples are created by keeping the A value the same (since A ↠ B), and swapping the B, D values between the two original tuples (since B ↠ D). This ensures that the multivalued dependencies are satisfied.