# Canonical Cover

Canonical Cover is the important topic of the Database Management System. Moreover, Freestudy9 has all kind of important topic and information about the subject.

**Consider following set F of functional dependencies on schema R(A**, **B, C) and compute canonical cover for F.**

**A -> BC, B -> C, A -> B and AB -> C Canonical cover: **

A canonical cover for F is a set of dependencies Fc such that

- F logically implies all dependencies in Fc, and
- Fc logically implies all dependencies in F, and
- No functional dependency in Fc contains an extraneous attribute, and
- Each left side of functional dependency in Fc is unique.

The algorithm to find Canonical cover:

To compute a canonical cover for F: repeat

Step 1: Use the union rule to replace any dependencies in F

α1 → β1 and α1 →β2 with α1 →β1 β2

Step 2: Find a functional dependency α→ β with an extraneous attribute either in α or in β

- If an extraneous attribute is found, delete it from AB→C until F does not change
- Note: Union rule may become applicable after some extraneous attributes have been deleted, so it has to be re-applied

*Steps to find Canonical Cover: *

Given : R = (A, B, C) and F = {A → BC, B → C, A → B, AB → C}

Step 1: Combine A → BC and A → B into A → BC Set is now {A → BC, B → C, AB → C}

Step 2: A is extraneous in AB → C

Also, Check if the result of deleting A from AB → C implied by the other dependencies

Yes: in fact, B → C is already present.

Set is now {A → BC, B → C}

##### Step 3: B is extraneous in A → BC

Check if A → C logically implied by A → B and the other dependencies Yes: using transitivity on A → B and B → C.

Set is now {A → B and B → C}

Can use attribute closure of A in more complex cases

The canonical cover is: A → B, B → C

**Related Terms**

DBMS Short Note, BCNF with Example, 3NF with Example, Engineering Study.

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