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4.Relations – Definition & Types
Class 11 • Mathematics • NCERT
Relations – Definition & Types
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This lesson introduces relations as defined in NCERT Class 11. Students learn ordered pairs, Cartesian products, definition of a relation, and different types of relations with simple examples and exam-focused questions.
Lesson Objectives
- Understand ordered pairs and Cartesian product.
- Define a relation between two sets.
- Identify different types of relations.
- Apply concepts to NCERT-style problems.
1. Ordered Pairs
An ordered pair is written as (a, b), where the order is important.
(a, b) ≠ (b, a) in general
Example: (2, 3) ≠ (3, 2)
Example: (2, 3) ≠ (3, 2)
2. Cartesian Product of Two Sets
If A and B are two non-empty sets, then the Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B.
If A = {1,2} and B = {3,4},
A × B = {(1,3), (1,4), (2,3), (2,4)}
A × B = {(1,3), (1,4), (2,3), (2,4)}
3. Definition of a Relation
A relation from set A to set B is a subset of the Cartesian product A × B.
If R ⊆ A × B, then R is a relation from A to B.
4. Types of Relations (NCERT)
• Empty Relation: No ordered pairs
• Universal Relation: A × B itself
• Identity Relation: (a, a) for all a ∈ A
• Inverse Relation: If (a, b) ∈ R, then (b, a) ∈ R⁻¹
• Universal Relation: A × B itself
• Identity Relation: (a, a) for all a ∈ A
• Inverse Relation: If (a, b) ∈ R, then (b, a) ∈ R⁻¹
Practice Questions (NCERT)
- What is an ordered pair?
- Is (2,3) equal to (3,2)?
- Define Cartesian product of two sets.
- If A = {1} and B = {2,3}, find A × B.
- What is a relation?
- Is every subset of A × B a relation?
- What is an empty relation?
- What is a universal relation?
- Define identity relation.
- What is an inverse relation?
✅ Show Answer Key
- A pair (a, b) where order matters.
- No.
- Set of all ordered pairs (a, b).
- {(1,2), (1,3)}
- A subset of A × B.
- Yes.
- A relation with no elements.
- A × B itself.
- Relation {(a, a) | a ∈ A}.
- Relation formed by reversing ordered pairs.
© Aviate Learning – Relations (NCERT Class 11)