NCERT Class 11 Mathematics Mathematics: Chapter 2 — RELATIONS AND FUNCTIONS
This chapter introduces the fundamental concepts of Relations and Functions in Mathematics. It begins by explaining the idea of patterns and links between quantities, drawing parallels to everyday relationships like brother-sister and mathematical ones like 'less than' or 'subset'. The chapter defines the Cartesian product of two non-empty sets, denoted as P × Q, which is the set of all ordered pairs of elements from P and Q. It illustrates this with examples involving colours and objects, and state codes and licence plates. The importance of order in ordered pairs is emphasized. The chapter also touches upon how these ordered pairs can represent points in a plane. The concept of function, a special type of relation, is highlighted as crucial for understanding mathematical correspondences. This foundational chapter prepares students for advanced mathematical concepts.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 11 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 2 — RELATIONS AND FUNCTIONS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 729 |
Learning outcomes
- Understand the concept of ordered pairs and Cartesian products of sets.
- Define and compute the Cartesian product of two non-empty sets.
- Recognize the importance of order in ordered pairs.
- Grasp the foundational idea of relations and functions in mathematics.
Vocabulary
| Word | Meaning |
|---|---|
| Ordered pair | A pair of elements written in small brackets and grouped together in a particular order, i.e., (p,q). |
| Cartesian product | The set of all ordered pairs of elements from two non-empty sets P and Q, denoted as P × Q. |
| Relation | A link or pattern between quantities or objects, often involving pairs. |
| Function | A special type of relation that captures a mathematically precise correspondence between quantities. |
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Practice questions
- If A = {1, 2} and B = {a, b}, find the Cartesian product A × B. Answer: A × B = {(1, a), (1, b), (2, a), (2, b)}
- Given sets X = {p, q} and Y = {r, s, t}, find the number of elements in X × Y. Answer: The number of elements in X × Y is |X| × |Y| = 2 × 3 = 6.
- Is the ordered pair (apple, red) the same as (red, apple)? Explain. Answer: No, the ordered pair (apple, red) is not the same as (red, apple) because the order of elements matters in an ordered pair.
Practice MCQs
Q1. What is the set of all ordered pairs of elements from two non-empty sets P and Q called?
Explanation: The set of all ordered pairs of elements from two non-empty sets P and Q is defined as the Cartesian product P × Q.
Q2. If , 2, 3} and , 5}, how many elements are in the Cartesian product A × B?
Explanation: The number of elements in the Cartesian product A × B is the product of the number of elements in A and B, which is |A| × |B| = 3 × 2 = 6.
Q3. Which of the following represents an ordered pair?
Explanation: An ordered pair is represented by enclosing the elements in small brackets, like (a, b).
Q4. For two sets A and B, when is A × B an empty set?
Explanation: If either set A or set B (or both) is the null set (empty set), their Cartesian product A × B will also be an empty set.
Frequently asked questions
What is an ordered pair in mathematics?
An ordered pair is a pair of elements written in small brackets and grouped together in a particular order, such as (p, q), where p is the first element and q is the second element.
How is the Cartesian product of two sets A and B defined?
The Cartesian product A × B is the set of all possible ordered pairs (a, b) where 'a' is an element of set A and 'b' is an element of set B.
What happens if one of the sets in a Cartesian product is empty?
If either set A or set B is the null set (empty set), then their Cartesian product A × B will also be an empty set.
Does the order of elements matter in a Cartesian product?
Yes, the order of elements is crucial in a Cartesian product. The ordered pair (a, b) is generally not the same as the ordered pair (b, a) unless a = b and both are in both sets.
What is the significance of the concept of a function?
The concept of a function is very important in mathematics as it precisely captures the idea of a correspondence between one quantity and another.
Related resources
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Topics covered
NCERT Class 11 Mathematics — Mathematics — Chapter 2 — RELATIONS AND FUNCTIONS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.