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## Closure of Attribute Set - Alternate Way / Closure of Attribute Set Algorithm / How do we find a key given a set of attributes? / How to find super key? / Attribute Closure in DBMS / Closure of Attributes Set Example

### To find the Closure of attribute/attribute set A, we have to do the following;

a) First of all find the set of all functional dependencies (F+) that are implied by a given set of functional dependencies (F).
b) Then take all the FDs from F+ that has A on the left hand side of the arrow.
C) Finally, find the union of right hand side of all those functional dependencies that have A on the left hand side. If the union includes all the attributes of the given relation R, then A is the key for the relation.

Example:
Assume a relation schema R = (A, B, C) with the set of functional dependencies F = {A B, B C}. Now, we can find the closure of attribute A as follows, according to this method;
Step 1: Find the F+.
F+ = { A B, B C, A C } [A C is derived using Transitivity rule]
Step 2: A B, and A C are the two functional dependencies that have common left hand side attribute A.
Step 3: The union of right hand sides ends with A BC. Hence, A is the one of the keys for the relation R.

• Simple.

### Drawbacks:

• The number of functional dependencies in F+ can be as many as 2n+1 where n is the number of attributes. It costs too much of time.

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