Hello,
I want to know if the following is an example of lossless decomposition, and why/why not?

R A B C
1 A 1000
2 B 2000
1 C 1000

The above is decomposed into:


A C
1 1000
2 2000
1 1000 and


B C
A 1000
B 2000
C 1000.

Will this be lossless? If so, why? If not, why not?



Thanks,
Prasanna

First I would start out by figuring out what lossless decomposition is.

Thanks for the reply. I understand what a lossless join is, but I am just confused with these types of examples. This particular example, on joining the 2 decomposed tables, it gives duplicate rows, but not rows that didn't exist at all in the original table.

It just gives rows which existed more than 1 time. Would it still be lossless?

Thanks,
Prasanna

It is a lossless join. Small world!!

The concept of lossless / lossy joins is part of relational database theory. Join in that context is an operation on relations and not "tables" of any other (non-relational) kind.

This:

looks like something that has duplicate tuples and therefore it isn't a relation and isn't a relational decomposition. If it isn't a relation then what you are describing can't be a join, let alone a lossless one. Of course it's quite possible to define joins and similar operations on tables (such as SQL tables) but then you'd also have to define what a lossless join meant in that same context. I'm not familiar with any such definition.