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Properties of Functional Dependency

1.  Reflexivity Property

2.  Transitive property

3.  Augmentation Property

4.  Union

5.  Splitting Property

6.  Another Property Composition

Example 1:

A → BCD then we can drive more FDs using the splitting property:

A → B, A → C, A → D, A → BC, A → CD, A → BD

Example 2:

If A → BCD so, can we say AB → CD is also FD because we can augment with B on both side

AB → BCD then using splitting property we can drive AB → CD.

So, we can drive all FDs from AB → BCD

Similarly, we can get if,

UGC NET 2013 (Dec)Q. 59.

Armstrong (1974) proposed a systematic approach to derive functional dependencies. Match the following with respect to functional dependencies:

List – I                                                           

a. Decomposition rule

b. Union rule

c. Composition rule

d. Pseudo transitivity rule       

List – II

i. If X → Y and Z → W then {X, Z} → {Y, W}

ii. If X → Y and {Y, W} → Z then {X, W} → Z

iii. If X → Y and X →  Z then X → {Y, Z}

iv. If X → {Y, Z} then X → Y and X → Z

Solution: 

(A)  Decomposition Rules or Splitting Rule: 

(B)  Union Rule:

(C)  Composition Rule:

(D)  Pseudo Transitivity Rule:      

So, option (D) is the correct answer.