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1.Relations – Types & Properties
Class 11 • Mathematics • NCERT
Relations – Types & Properties
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This lesson introduces relations, their types, and properties as prescribed by NCERT Class 11. Students learn how ordered pairs form relations and how properties help classify them.
Lesson Objectives
- Understand the concept of relations.
- Identify different types of relations.
- Learn properties of relations.
- Apply concepts to exam-style questions.
1. What Is a Relation?
A relation from a set A to a set B is a subset of the Cartesian product A × B.
If (a, b) ∈ R, then a is related to b.
2. Types of Relations
• Empty relation: No element is related
• Universal relation: All possible ordered pairs
• Identity relation: (a, a) for all a ∈ A
• Inverse relation: If (a, b) ∈ R then (b, a) ∈ R⁻¹
• Universal relation: All possible ordered pairs
• Identity relation: (a, a) for all a ∈ A
• Inverse relation: If (a, b) ∈ R then (b, a) ∈ R⁻¹
3. Reflexive Relation
A relation R on set A is reflexive if (a, a) ∈ R for all a ∈ A.
Example: Equality relation on a set
4. Symmetric Relation
A relation R is symmetric if (a, b) ∈ R implies (b, a) ∈ R.
Example: Relation “is a sibling of”
5. Transitive Relation
A relation R is transitive if (a, b) ∈ R and (b, c) ∈ R implies (a, c) ∈ R.
Example: “greater than” relation
6. Equivalence Relation
A relation that is reflexive, symmetric, and transitive is called an equivalence relation.
Practice Questions (NCERT)
- Define a relation.
- What is an identity relation?
- Define reflexive relation.
- Define symmetric relation.
- Define transitive relation.
- What is an equivalence relation?
- Is empty relation reflexive?
- Give one example of symmetric relation.
- Can a relation be reflexive and not symmetric?
- Is this topic part of NCERT Class 11 syllabus?
✅ Show Answer Key
- Subset of Cartesian product
- Relation containing (a, a) for all a
- (a, a) ∈ R for all a
- (a, b) ∈ R ⇒ (b, a) ∈ R
- (a, b), (b, c) ∈ R ⇒ (a, c) ∈ R
- Reflexive + Symmetric + Transitive
- No
- Sibling relation
- Yes
- Yes
© Aviate Learning – Relations & Functions (NCERT Class 11)