# Decomposition in DBMS – Lossless and Lossy

Decomposition means dividing a large and complex table into multiple small and easy tables. This removes redundancy, anomalies, and inconsistency in a database. This is the first stage of normalization.

Suppose we have a relational schema R, in which we have attributes as given below:

A1, A2, A3…………An

So R = {A1, A2, A3…………An}

If we decompose it into small parts then R will be divided into the following parts:

R1, R2……..Rx

These all relational schemas belong to the original one R.

R1, R2……..Rx = R

Also, we can write that union of all these subsets belongs to the original set R.

R1 U R2 U R3 ……..U Rx = R

Here R1, R2……..Rx <= R

Also 1<= i <= x      (i= number of relation like 1,2,3…..x)

Decomposition is further divided into two parts Lossless and Lossy. Let’s discuss them one by one in detail.

## Lossless Decomposition

Loss means data loss while decomposing a relational table. A lossless decomposition is somewhat in which data is not lost because JOIN is used.

First, we decompose a large table into small appropriate tables, then apply natural join to reconstruct the original table.

This is a student database relational table:

Student Details

We can decompose it into two simple tables as given below:

Student Subject Details:

Student Personal Details:

If we want to see a common table then we can apply Natural JOIN between both tables like this:

Student Subject Details ⋈ Student Personal Details

In this operation, no data loss occurs, so this is a good option to consider for decomposition.

## Lossy Decomposition

In this, the decomposition is performed in such a manner that the data will be lost. Let’s take an example:

Student Details

If we divide this student details table into two sections as given below:

Student Subject Details:

Student Personal Details:

In this Student Personal Details table, the SID column is not included, so now we don’t know that these mobiles numbers and address belongs to whom.

So always decompose a table in such a manner that the data may be easily reconstructed and retrieved.