In another class having 2 sections, the two respective class representatives have prepared 2 separate Sports Preferences tables, as shown below:
Sports preference of section 1 (arranged on roll number column) Table: Sports Preferences
| Roll_no | Sports |
|---|---|
| 9 | Cricket |
| 13 | Football |
| 17 | Badminton |
| 21 | Hockey |
| 24 | Cricket |
Sports preference of section 2 (arranged on Sports name column, and column order is also different) Table: Sports Preferences
| Sports | Roll_no |
|---|---|
| Badminton | 17 |
| Cricket | 9 |
| Cricket | 24 |
| Football | 13 |
| Hockey | 21 |
Are the states of both the relations equivalent? Justify.
Yes, the states of both relations are equivalent.
In a relational database, a relation is defined as a set of tuples. As per the properties of relations, the order of tuples (rows) is immaterial because a set does not have any order. Similarly, the order of attributes (columns) is also immaterial because attributes are identified by their names, not by their positions.
Both tables contain the same data — the same five tuples with identical attribute values: (Roll_no: 9, Sports: Cricket), (Roll_no: 13, Sports: Football), (Roll_no: 17, Sports: Badminton), (Roll_no: 21, Sports: Hockey), and (Roll_no: 24, Sports: Cricket). The only differences are the arrangement of rows and the order of columns, which do not affect the state of a relation. Hence, both relations represent the same state.
Explanation
This question tests the fundamental properties of relations in relational database theory. The key concept is that a relation is a mathematical set of tuples, and sets are unordered by definition. Therefore, neither row order nor column order affects the equivalence of two relations. Students should recognize that both tables represent the same set of tuples with identical attribute-value pairs, making them equivalent states.
Solution Steps
Step 1: Identify that both tables contain the same tuples with same attribute values.
Step 2: Apply the property that row order is immaterial in a relation.
Step 3: Apply the property that column order is immaterial in a relation.
Step 4: Conclude that both relations are equivalent since they represent the same set of tuples.