self_doubt

Question

If a relation is decomposed into more than two relations then what is the correct method to check whether the decomposition is lossless or not? Can we use R1⋂R2→R1 or R1⋂R2→R2 pairwise for the decomposition or is there any other method?

Answer 1

Say a relation R(A,B,C,D,E) is decomposed into 3 relations - R1(A,B,C), R2(C,D), R3(D,E)_.

Take an two decompositions first. I am taking R1 and R2.

Find the closure of the common attribute(s) i.e. (C⁺) and see if C is a key of any of R1 or R2. If yes, join R1 and R2 to a new relation, say R12 (A,B,C,D).

Now we have two relations R12(A,B,C,D) and R3(D,E). Again take the common attribute(s) and apply closure.

This can be repeated for any number of relations.