Understanding Common Terms And Concepts

Apologies for any confusion earlier. Let’s reevaluate.

In order for the decomposition to have the lossless join property, we need to ensure that every combination of tuples from the decomposed relations can be joined together to reconstruct the original relation without losing any information.

1. R1(B, C, H) with the FD H->BC
2. R2(A, B, K) with the FD BK->AC
3. R3(A, B, I) without any FD provided

After joining R1 and R2 on B, we have a relation with attributes (A, B, C, H, K).

Now, to join this intermediate result with R3, we notice there are no common attributes between them. This means the join would result in an empty relation, and we wouldn’t be able to reconstruct the original relation R.

Since not every combination of tuples from the decomposed relations can be joined together to reconstruct R, the decomposition does not maintain the lossless join property.

So, the correct assessment is