For relation R = (L, M, N, O, P), the following dependencies hold: { M → O, NO…

Conclusion: The decomposition is lossless and not dependency preserving.

• Lossless-join check: The intersection of the two decomposed schemas (L,M,N,P) and (M,O) is {M}. Because the FD M → O is in the given set, M functionally determines both attributes of the second relation (M,O). Therefore the intersection functionally determines one of the relations, which satisfies the lossless-join condition. Hence the decomposition is lossless.

• Dependency preservation check: The original FDs are M → O, NO → P, P → L, and L → MN. Projecting these onto the decomposed relations gives:

  • Onto (L, M, N, P): P → L and L → MN.

  • Onto (M, O): M → O.

  The FD NO → P involves attributes from both relations (N and O on one side, P on the other) and is not present in either projection. It also cannot be derived from the projected FDs: using the projected FDs, the closure of {N,O} is only {N,O}, so P is not implied. Therefore NO → P is not preserved, and the decomposition is not dependency preserving.