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3.Venn Diagrams & Applications
Class 11 • Mathematics • NCERT
Venn Diagrams & Applications
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This lesson introduces Venn diagrams as a visual tool to represent sets and their relationships. Students learn how to use Venn diagrams to solve simple problems involving union, intersection, and difference strictly as per NCERT Class 11.
Lesson Objectives
- Understand what a Venn diagram is.
- Represent sets using Venn diagrams.
- Solve problems using union and intersection.
- Apply Venn diagrams to simple word problems.
1. What Is a Venn Diagram?
A Venn diagram is a diagram that uses circles to represent sets and shows the relationship between them.
• Universal set is represented by a rectangle
• Sets are represented by circles inside the rectangle
• Sets are represented by circles inside the rectangle
2. Representation of Union and Intersection
Venn diagrams help us clearly see common and combined elements.
Union (A ∪ B): All elements in A or B
Intersection (A ∩ B): Elements common to both A and B
Intersection (A ∩ B): Elements common to both A and B
3. Difference of Sets Using Venn Diagrams
The difference of two sets shows elements belonging to one set only.
A − B: Elements in A but not in B
B − A: Elements in B but not in A
B − A: Elements in B but not in A
4. Applications of Venn Diagrams
Venn diagrams are used to solve word problems involving two sets.
Example (NCERT style):
In a class, some students play cricket, some play football, and some play both. Venn diagrams help find the number of students in each group.
In a class, some students play cricket, some play football, and some play both. Venn diagrams help find the number of students in each group.
Practice Questions (NCERT)
- What shape represents the universal set in a Venn diagram?
- What shape represents a set?
- Which region shows A ∩ B?
- Which region represents A − B?
- What does A ∪ B represent?
- If A = {1,2} and B = {2,3}, find A ∩ B.
- Find A ∪ B for the above sets.
- Is Venn diagram useful for showing relationships between sets?
- Can Venn diagrams represent empty sets?
- Are Venn diagrams used in NCERT problems?
✅ Show Answer Key
- Rectangle
- Circle
- Overlapping region
- Region of A excluding overlap
- All elements in A or B
- {2}
- {1,2,3}
- Yes
- Yes
- Yes
© Aviate Learning – Sets (NCERT Class 11)