What is a lossless-join decomposition?

• A. Lossless-join means you can reconstruct the original relation only if you know the original schema.
• B. Joining the decomposed relations yields the original relation without spurious tuples.
• C. The decomposition reduces all data to a single table.
• D. The decomposition guarantees zero redundancy.

Answer: (B)

When you split a relation into smaller parts, you want to be able to put it back together exactly as it was, without creating any extra or invalid rows. That capability is what a lossless-join decomposition guarantees: joining the decomposed relations yields exactly the original relation, with no spurious tuples.

A practical way this works is by ensuring the overlap between the pieces is a key for one (or more) of them. For example, if you have a relation with attributes A, B, and C, and you decompose into R1(A, B) and R2(A, C) where A is the key in the original context, joining R1 and R2 on A will reproduce every original row and won’t generate new combinations that weren’t in the original data. This keeps data integrity intact while still allowing you to break the table into smaller, more manageable pieces.

It’s important to distinguish this from the idea of zero redundancy. A lossless-join decomposition doesn’t necessarily eliminate all redundancy on its own; it ensures that you can recover the exact original data after a join. Other decompositions can be lossless but still introduce redundant data, depending on the design. And it’s not about needing special knowledge of the original schema to reconstruct; it’s about the join property itself preserving exactly the original tuples.