Candidate keys and super keys are concepts in relational database theory that relate to the uniqueness and irreducibility of attributes within a table's schema.
1. **Super Key**:
- A super key is a set of one or more attributes (columns) that uniquely identifies each tuple (row) within a table.
- It may contain more attributes than necessary to uniquely identify tuples.
- A super key must satisfy the uniqueness property, meaning no two tuples in the table can have the same combination of values for the attributes in the super key.
- Super keys can be minimal (irreducible) or non-minimal (reducible).
2. **Candidate Key**:
- A candidate key is a minimal super key, meaning it is a super key with the fewest possible attributes.
- It uniquely identifies each tuple in the table.
- If any attribute is removed from a candidate key, it loses its uniqueness property.
- Each candidate key within a table is unique, meaning no two candidate keys contain the same set of attributes.
Now, let's delve deeper into the uniqueness and irreducibility properties that differentiate between candidate keys and super keys:
- **Uniqueness**:
- Both candidate keys and super keys must guarantee uniqueness.
- However, candidate keys provide the strongest form of uniqueness because they are minimal and cannot be further reduced without losing the uniqueness property.
- Super keys, on the other hand, may contain redundant attributes that do not contribute to uniqueness, but they still ensure that each tuple in the table is uniquely identifiable.
- **Irreducibility**:
- Irreducibility refers to the inability to remove any attribute from a key without losing its unique identification property.
- Candidate keys are by definition irreducible because they are minimal super keys.
- Super keys, while they can also provide uniqueness, may include additional attributes that are not strictly necessary for uniquely identifying tuples. Removing these attributes may still preserve uniqueness, making them reducible.
In summary, while both candidate keys and super keys ensure uniqueness, candidate keys are distinguished by their irreducibility, as they represent the smallest set of attributes necessary to uniquely identify each tuple in a table. Super keys, while also ensuring uniqueness, may contain redundant attributes and are not necessarily minimal.
Understanding with example:
Let's consider a simple table representing employees in a company:
**Employee Table:**
| EmployeeID | Name | Department | Salary |
|------------|-----------|------------|--------|
| 1 | John | HR | 50000 |
| 2 | Jane | IT | 60000 |
| 3 | Alice | IT | 55000 |
| 4 | Bob | Sales | 48000 |
**1. Uniqueness:**
- **Candidate Key Example:**
In this table, the attribute `EmployeeID` serves as a candidate key because it uniquely identifies each employee. No two employees have the same `EmployeeID`.
Candidate Key: `{EmployeeID}`
- **Super Key Example:**
A super key could be the combination of `EmployeeID` and `Name`. This combination uniquely identifies each employee, making it a super key. However, it's not minimal because `EmployeeID` alone is sufficient.
Super Key: `{EmployeeID, Name}`
**2. Irreducibility:**
- **Irreducible Candidate Key Example:**
`EmployeeID` is an irreducible candidate key because removing any attribute from it would violate uniqueness. If you remove `EmployeeID`, you can't uniquely identify employees anymore.
Candidate Key: `{EmployeeID}`
- **Reducible Super Key Example:**
Let's consider the super key `{EmployeeID, Department}`. While it uniquely identifies each tuple, `Department` is not necessary for uniqueness. Removing `Department` still leaves us with a unique identifier.
Super Key (Reducible): `{EmployeeID, Department}`
In summary, `EmployeeID` serves as both a candidate key and an example of irreducibility. Meanwhile, combinations like `{EmployeeID, Name}` represent super keys but are not minimal due to the inclusion of non-essential attributes.
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