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2NF , 3NF, BCNF decomposition allowed if lossless and dependency preserving , both conditions must preserve. Otherwise given decomposition wrong for normal forms. Is this statement correct????

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The statement is mostly correct, but it needs some clarification.

In the process of database normalization, the goal is to decompose a relation (table) into smaller relations that are in higher normal forms (e.g., from 1NF to 2NF, 3NF, BCNF, etc.) while preserving the functional dependencies and avoiding data anomalies.

A decomposition is said to be lossless if the original relation can be reconstructed from the smaller relations using a join operation. A decomposition is said to be dependency preserving if it preserves all the functional dependencies of the original relation.

If a decomposition is both lossless and dependency preserving, then it is considered a valid decomposition. However, if a decomposition is not lossless or not dependency preserving, then it may lead to data anomalies, and it is considered a wrong decomposition.

Therefore, the statement "2NF, 3NF, BCNF decomposition allowed if lossless and dependency preserving, both conditions must preserve. Otherwise given decomposition is wrong for normal forms" is mostly correct. However, it is important to note that not all decompositions that satisfy the lossless and dependency preserving conditions are necessarily in higher normal forms. Some decompositions may introduce redundant relations, and some may not be in the highest normal form possible. Therefore, it is important to carefully evaluate the decompositions and choose the one that minimizes redundancy and maximizes the normal form.

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