# Can there be more than one Bcnf decomposition?

## Can there be more than one Bcnf decomposition?

There is sometimes more than one BCNF decomposition of a given schema. The algorithm given produces only one of these possible decompositions. Some of the BCNF decompositions may also yield dependency preservation, while others may not.

## Is Bcnf decomposition dependency preserving?

To convert this relation into bcnf decompose into two relations : R1(a b ) {a->b} key = a R2(a c d e) {ac->de} key =a Both R1 and R2 are in bcnf as every determinant is a key, but they are not dependency preserving as bd->e is lost.

## How do you decompose a relation into BCNF?

Example in Decomposition into BCNF

1. Relation: A B C D E F G H I J K L M Functional dependencies: A -> B C D E E -> F G H I -> J A I -> K A L -> M.
2. First: Find all keys.
3. Check R for BCNF condition:
4. Decompose:
5. Check R1 for BCNF condition:
6. Decompose:
7. Check R11 for BCNF condition:
8. Check R12 for BCNF condition:

## Is a BCNF decomposition always lossless?

The decomposition of R into X and Y is lossless with respect to F if and only if the closure of F contains: X ∩ Y → X, or X ∩ Y → Y in example: decomposing ABC into AB and BC is lossy, because intersection (i.e., “B”) is not a key of either resulting relation.

## Which decomposition gives a lossless join?

Relation R is decomposed into two or more relations if decomposition is lossless join as well as dependency preserving. 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.

## Which normal form has lossless decomposition?

The join returns more tuples than the original relation “Lossy” refers not to the loss of tuples, but to the loss of information (the ability to distinguish different states of the original relation) FD is what makes a decomposition lossless!

## What is a BCNF violation?

Informally, a relation is in BCNF if and only if the arrow in every FD is an arrow out of a candidate key. In other words, a relation is in BCNF if and only if the left-hand side of every functional dependency is a candidate key. The left-hand side of C->AF is C, but C is not a candidate key.

## How do you solve lossless decomposition?

Solution: For a relation R to be lossless decomposition, R should satisfy following three conditions:

1. Attribute(R1) U Attribute (R2) = Attribute (R)
2. Attribute (R1) ∩ Attribute (R2) ≠ Φ
3. Attribute (R1) ∩ Attribute (R2) -> Attribute (R1) or Attribute (R1) ∩ Attribute (R2) -> Attribute (R2)

## What is lossless join decomposition explain with an example?

such that a natural join of the two smaller relations yields back the original relation. This is central in removing redundancy safely from databases while preserving the original data.

## What is the lossless join property of decomposition Why is it important?

The lossless join property is a feature of decomposition supported by normalization. It is the ability to ensure that any instance of the original relation can be identified from corresponding instances in the smaller relations.

## Which of the following is NOT type of decomposition?

H2+Cl2→2HCl is not a decomposition reaction. It is a combination reaction.

## What is the dependency preservation property for a decomposition Why is it important?

Dependency Preserving It is an important constraint of the database. In the dependency preservation, at least one decomposed table must satisfy every dependency.

## What are the rules for decomposing a relation?

The properties of a relational decomposition are listed below :

• Attribute Preservation: Using functional dependencies the algorithms decompose the universal relation schema R in a set of relation schemas D = { R1, R2, …..
• Dependency Preservation:
• No redundancy:
• Lossless Join:

## How do you calculate dependency preservation?

Consider a relation R R —> F{…with some functional dependency(FD)….} R is decomposed or divided into R1 with FD { f1 } and R2 with { f2 }, then there can be three cases: f1 U f2 = F —–> Decomposition is dependency preserving.

## How lossless decomposition is useful in database?

Decomposition is lossless if it is feasible to reconstruct relation R from decomposed tables using Joins. This is the preferred choice. The information will not lose from the relation when decomposed. The join would result in the same original relation.

## What is the difference between lossy and lossless decomposition?

This decomposition is Lossy. Thus, we can figure out whether a decomposition is lossless or lossy….Difference Between Lossless and Lossy Join Decomposition :

Lossless Lossy
The common attribute of the sub relations is a superkey of any one of the relation. The common attribute of the sub relation is not a superkey of any of the sub relation.

## What is required property of decomposition?

Properties of Decomposition. Decomposition must be lossless. It means that the information should not get lost from the relation that is decomposed. It gives a guarantee that the join will result in the same relation as it was decomposed.

## What are the uses of closure algorithm?

Several uses of attribute closure: 1. Used to check whether an attribute (or set of attributes) forms a key or not. Use the algorithm discussed in the posts “How to find closure of attributes in DBMS?” Or “How to find key of a given table? – Analternate way”. 2.

## What is closure method?

A closure is the combination of a function bundled together (enclosed) with references to its surrounding state (the lexical environment). In other words, a closure gives you access to an outer function’s scope from an inner function.

## What is closure of F give example?

The Closure Of Functional Dependency means the complete set of all possible attributes that can be functionally derived from given functional dependency using the inference rules known as Armstrong’s Rules. If “F” is a functional dependency then closure of functional dependency can be denoted using “{F}+”.

## What is the benefit of attribute closure?

If attribute closure of an attribute set contains all attributes of relation, the attribute set will be super key of the relation. If no subset of this attribute set can functionally determine all attributes of the relation, the set will be candidate key as well.

## How do you find closure?

The closure of a set of attributes X is the set of those attributes that can be functionally determined from X. The closure of X is denoted as X+. When given a closure problem, you’ll have a set of functional dependencies over which to compute the closure and the set X for which to find the closure.

## What do you mean by closure of attribute?

Closure of an Attribute: Closure of an Attribute can be defined as a set of attributes that can be functionally determined from it. OR. Closure of a set F of FDs is the set F+ of all FDs that can be inferred from F.

## What is closure method in DBMS?

A Closure is a set of FDs is a set of all possible FDs that can be derived from a given set of FDs. It is also referred as a Complete set of FDs. If F is used to donate the set of FDs for relation R, then a closure of a set of FDs implied by F is denoted by F+.

## What is F+ in DBMS?

Definition. The closure of F, denoted as F+, is the set of all regular FDs that can be derived from F. Do not confuse the closure of F with the closure of an attribute set.

## What is fully functional dependency in DBMS?

A full functional dependency is a state of database normalization that equates to the normalization standard of Second Normal Form (2NF). In brief, this means that it meets the requirements of First Normal Form (1NF), and all non-key attributes are fully functionally dependent on the primary key.

## What is functional dependency DBMS?

A functional dependency (FD) is a relationship between two attributes, typically between the PK and other non-key attributes within a table. For any relation R, attribute Y is functionally dependent on attribute X (usually the PK), if for every valid instance of X, that value of X uniquely determines the value of Y.

## What is functional dependency give an example?

By Chaitanya Singh | Filed Under: DBMS. The attributes of a table is said to be dependent on each other when an attribute of a table uniquely identifies another attribute of the same table. For example: Suppose we have a student table with attributes: Stu_Id, Stu_Name, Stu_Age.

## What are the four types of dependencies?

There are 4 types of dependencies in project management viz. Mandatory, Discretionary, External, & Internal.

## How many types of functional dependency are there?

four types

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