What is the minimum number of decomposition required to make the above relation bcnf?
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perm_identity
Lossless Join and Dependency Preserving Decomposition

Decomposition of a relation is done when a relation in relational model is not in appropriate normal form. Relation R is decomposed into two or more relations if decomposition is lossless join as well as dependency preserving.
Lossless Join Decomposition
If we decompose a relation R into relations R1 and R2,
Decomposition is lossy if R1 ⋈ R2 ⊃ R
Decomposition is lossless if R1 ⋈ R2 = R
To check for lossless join decomposition using FD set, following conditions must hold:
Union of Attributes of R1 and R2 must be equal to attribute of R. Each attribute of R must be either in R1 or in R2. Att(R1) U Att(R2) = Att(R)
Intersection of Attributes of R1 and R2 must not be NULL. Att(R1) ∩ Att(R2) ≠ Φ
Common attribute must be a key for at least one relation (R1 or R2) Att(R1) ∩ Att(R2) -> Att(R1)
perm_identity
Lossless Join and Dependency Preserving Decomposition

Decomposition of a relation is done when a relation in relational model is not in appropriate normal form. Relation R is decomposed into two or more relations if decomposition is lossless join as well as dependency preserving.
Lossless Join Decomposition
If we decompose a relation R into relations R1 and R2,
Decomposition is lossy if R1 ⋈ R2 ⊃ R
Decomposition is lossless if R1 ⋈ R2 = R
To check for lossless join decomposition using FD set, following conditions must hold:
Union of Attributes of R1 and R2 must be equal to attribute of R. Each attribute of R must be either in R1 or in R2. Att(R1) U Att(R2) = Att(R)
Intersection of Attributes of R1 and R2 must not be NULL. Att(R1) ∩ Att(R2) ≠ Φ
Common attribute must be a key for at least one relation (R1 or R2) Att(R1) ∩ Att(R2) -> Att(R1)
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