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Database-Management-System
August 29, 2024
Functional-Dependency
August 29, 2024
Database-Management-System
August 29, 2024
Functional-Dependency
August 29, 2024

Database-Management-System

Question 672
Consider a schema R(MNPQ) and functional dependencies M → N, P → Q. Then the decomposition of R into R​ 1​ (MN) and R​ 2​ (PQ) is________.
A
Dependency preserving but not lossless join
B
Dependency preserving and lossless join
C
Lossless join but not dependency preserving
D
Neither dependency preserving nor lossless join.
Question 672 Explanation: 
Definition of lossless decomposition:​ Let R be the relational schema decomposed into R​ 1
and R​ 2​ . Given decomposition is lossless only if
1. R​ 1​ U R​ 2​ =R
2. R​ 1​ U R​ 2​ =φ
3. R​ 1 ∩ R​ 2​ → R​ 1 ​ (or) R​ 1 ∩ R​ 2​ → R​ 2
→ In this schema, there is no common key attribute between R​ 1​ and R​ 2​ . So, this relation is lossy relation.
Definition of Functional dependency preserving:
→ Let R be the relational schema with functional dependency set F is decomposed into R​ 1​ , R​ 2​ ,..,R​ n ​ with functional dependency sets F​ 1​ ,F​ 2​ ,…,F​ n​ respectively. In general F​ 1​ ,F​ 2​ ,…,F​ n ​ can be ⊆ F.
So, dependencies are preserved in the given decomposition.
Correct Answer: A
Question 672 Explanation: 
Definition of lossless decomposition:​ Let R be the relational schema decomposed into R​ 1
and R​ 2​ . Given decomposition is lossless only if
1. R​ 1​ U R​ 2​ =R
2. R​ 1​ U R​ 2​ =φ
3. R​ 1 ∩ R​ 2​ → R​ 1 ​ (or) R​ 1 ∩ R​ 2​ → R​ 2
→ In this schema, there is no common key attribute between R​ 1​ and R​ 2​ . So, this relation is lossy relation.
Definition of Functional dependency preserving:
→ Let R be the relational schema with functional dependency set F is decomposed into R​ 1​ , R​ 2​ ,..,R​ n ​ with functional dependency sets F​ 1​ ,F​ 2​ ,…,F​ n​ respectively. In general F​ 1​ ,F​ 2​ ,…,F​ n ​ can be ⊆ F.
So, dependencies are preserved in the given decomposition.
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