In mathematics and data representation, a relation is often written as a set of ordered pairs:
Example:
[
R = {(2, 5), (3, 6), (4, 9), (5, 12)}
]
But sometimes, instead of writing it as a set, we want to represent the same relation in a table.
✅ A table is just another way of showing the same information.
Nothing changes — only the format.
Step-by-Step: Convert a Set into a Table
Suppose we have a set of ordered pairs:
[
A = {(1, 2), (2, 4), (3, 6), (4, 8)}
]
Each ordered pair is structured as:
✅ (x, y)
→ x = input
→ y = output
✅ Now create a table:
| x | y |
| – | – |
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |
✅ This table represents the same relation as the set.
Another Example
Set:
[
R = {(a, 1), (b, 2), (c, 3)}
]
Table:
| First Element | Second Element |
|---|---|
| a | 1 |
| b | 2 |
| c | 3 |
✔ Both represent the same relation
✔ Only the format changed
Why Create a Table from a Set?
| Reason | Benefit |
|---|---|
| Easier to read | Cleaner format than list of pairs |
| Compare values | Quickly see patterns or repeats |
| Domain & Range clear | Inputs and outputs visible |
| Used in databases | Tables are standard data format |
Example With Domain and Range
Set of ordered pairs:
[
S = {(2, 10), (3, 15), (4, 20)}
]
Table:
| x (Domain) | y (Range) |
|---|---|
| 2 | 10 |
| 3 | 15 |
| 4 | 20 |
✅ Domain = {2, 3, 4}
✅ Range = {10, 15, 20}
Real-World Use
Relations and tables are not only math — they are used in databases, programming, and data science.
Example from a school database:
Set as ordered pairs:
[
{(Ali, 85), (Sara, 92), (Umer, 78)}
]
Table:
| Student | Score |
|---|---|
| Ali | 85 |
| Sara | 92 |
| Umer | 78 |
✅ Same relation → different representation
Helpful Links
- Khan Academy: https://www.khanacademy.org/math/algebra
- Math Is Fun: https://www.mathsisfun.com/sets/relations.html
FAQs
1. Which table represents the same relation as the set?
Any table that lists the first element in one column and the second element in another column represents the same relation. The values do not change — only the format does.
2. How do you turn a set of ordered pairs into a table?
Write the first value of each pair in column 1 and the second value in column 2. Each ordered pair becomes one row.
3. What are ordered pairs in a relation?
Ordered pairs show a connection between two values. The first is input (x), the second is output (y). Example: (3, 9).
4. What is the domain and range of a relation?
- Domain = all x-values (inputs)
- Range = all y-values (outputs)
They can be found easily from a table.
5. Why is table representation important?
Tables make data easy to read, compare, calculate, and store — especially in databases and statistics.
Final Summary
✔ A set of ordered pairs and a table can represent the same relation
✔ Simply rewrite each pair as a row
✔ This method is useful in math, statistics, and computer science
✔ Tables are easier to read and analyze