Explain the closure of attribute sets.
Subject
Database Management System
Standard
Computer Science Engineering
Views
669
Asked By
Deepak
Answer / Solution
In the context of databases, the closure of attribute sets refers to the process of determining all the attributes that can be functionally determined by a given set of attributes. It is also known as the closure of a set of functional dependencies or the attribute closure.
To understand attribute closure, let's consider an example. Suppose we have a relation (table) called "Employees" with the following attributes:
Employees (EmpID, EmpName, EmpAddress, EmpPhone, Salary)
Let's say we have the following functional dependencies:
- EmpID -> EmpName, EmpAddress
- EmpID -> EmpPhone
- EmpPhone -> Salary
The closure of an attribute set refers to the set of all attributes that can be determined by that attribute set using the given functional dependencies.
For example, let's find the closure of the attribute set {EmpID} using the given functional dependencies:
Step 1: Initially, we have {EmpID}.
Step 2: Using the functional dependencies, we see that EmpID -> EmpName, EmpAddress (from FD 1).
Step 3: We add EmpName and EmpAddress to the set, so now we have {EmpID, EmpName, EmpAddress}.
Step 4: Again, using the functional dependencies, we find that EmpID -> EmpPhone (from FD 2).
Step 5: We add EmpPhone to the set, so now we have {EmpID, EmpName, EmpAddress, EmpPhone}.
Step 6: Finally, using the last functional dependency, EmpPhone -> Salary (from FD 3), we find that EmpID -> Salary.
Step 7: We add Salary to the set, and now we have the closure {EmpID, EmpName, EmpAddress, EmpPhone, Salary}.
So, the closure of the attribute set {EmpID} in the Employees relation is {EmpID, EmpName, EmpAddress, EmpPhone, Salary}.
The closure of an attribute set is important in database design as it helps in determining the minimal set of attributes needed to form a key, identifying functional dependencies, and normalizing relations.
Answer / Solution
To understand attribute closure, let's consider an example. Suppose we have a relation called "Employee" with the following attributes:
Employee (EmployeeID, Name, Department, Salary)
Now, let's assume the following functional dependencies:
- EmployeeID → Name
- EmployeeID → Department
- Department → Salary
These functional dependencies indicate that the value of "EmployeeID" uniquely determines the values of "Name" and "Department," and the value of "Department" uniquely determines the value of "Salary."
To find the closure of an attribute set, we start with the initial set of attributes and iteratively apply the functional dependencies until no more attributes can be derived.
Let's say we want to find the closure of the attribute set {EmployeeID}:
Step 1: Start with the initial set of attributes: {EmployeeID}
Step 2: Apply the functional dependencies: - EmployeeID → Name (Add Name to the set) - EmployeeID → Department (Add Department to the set) - Department → Salary (Add Salary to the set)
Step 3: Check if any new attributes were added in Step 2. - Since new attributes were added, repeat Step 2.
Step 4: Apply the functional dependencies again: - EmployeeID → Name (Already present) - EmployeeID → Department (Already present) - Department → Salary (Already present)
Step 5: No new attributes were added in Step 4, so the closure of {EmployeeID} is {EmployeeID, Name, Department, Salary}.
The closure of the attribute set {EmployeeID} includes all attributes that can be determined by the given functional dependencies. In this case, the closure includes EmployeeID, Name, Department, and Salary.
It's important to note that closures can also be used to determine the keys and superkeys of a relation, which are essential for database design and normalization.
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