## Dependency preserving decomposition - Dependency preserving decomposition solved exercises - How to verify that a decomposition is dependency preserving? - Steps to find dependency preserving decomposition - Dependency preserving decomposition examples

**Dependency preserving decomposition**
Consider a relation R (A, B, C, D)
with the following set of functional dependencies;

F = {A → B, B → C, and C → D}.

Is the decomposition of R (A, B, C, D)
into R1 (A, B, C) and R2 (C, D) a dependency preserving decomposition?

**Solution:**
The above said decomposition of R into
R1 and R2 is a dependency preserving decomposition if (F

_{1}U F_{2})^{+}= F^{+}, where F_{1}is set of FDs hold by R1, F_{2}is set of FDs hold by R2, and F is the set of FDs hold by R.*: for R1, the derivable non-trivial functional dependencies are, A → B, and B → C. Hence, F*

**Step 1**_{1}= {A → B, B → C}

*: for R2, the derivable non-trivial functional dependency is, C → D. Hence, F*

**Step 2**_{2}= {C → D}

(

**F**) = ({A → B, B → C} U {C → D}) = {A → B, B → C, C → D} =_{1}U F_{2}**F**.
F

_{1}U F_{2}and F both have same set of functional dependencies. Hence, the decomposition of R (A, B, C, D) into R1 (A, B, C) and R2 (C, D) a dependency preserving decomposition.
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