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If a relational schema is in BCNF then all redundancy based on functional dependency has been removed, although other types of redundancy may still exist.

(I) A relational schema R is in BCNF form if and only if for every one of its dependencies X → Y, at least one of the following conditions hold :
1. X → Y is a trivial functional dependency i.e. Y is a subset of X .
2. X is a super key for schema R

So, we check transitive dependency for only non-prime attributes in case of BCNF.

Thus, I is false.

(II) A relation R is in 3NF if every non-prime attribute of R is fully functionally dependent on some key of R, not for all.. 

II is false

III is true

answer is 2

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Minimum relations to decompose into BCNF and 4NF.List only relation names with attributes and total number of relations