Show that it is possible to ensure that a dependency-preserving decomposition into 3NF is a lossless decomposition by guaranteeing that at least one schema contains a candidate key for the schema...

Show that it is possible to ensure that a dependency-preserving decomposition

into 3NF is a lossless decomposition by guaranteeing that at least one schema

contains a candidate key for the schema being decomposed. (Hint: Show that

the join of all the projections onto the schemas of the decomposition cannot

have more tuples than the original relation.)