## 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;

*To find the Closure of attribute/attribute set A*

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.

### Advantages:

- Simple.

### Drawbacks:

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