Various uses of attribute closure

What are the uses of attribute closure A⁺ / Purposes of finding attribute closure / Attribute closure in DBMS

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. Used to find easily all the functional dependencies hold in a relation.

For example, to check whether a FD like A → B holds in a relation, find the A⁺. If B is in A⁺, then the functional dependency A → B is valid.

3. Used as an alternate way to find Closure of FDs (F⁺).

For every attribute or set of attributes on the left hand side of the arrow in a functional dependency, find the Closure. This process results in F⁺.

Very very useful link in knowing closure, canonical cover, normalization etc.