Venn Diagrams Class 6 ICSE — Chapter 30
Venn diagrams class 6 ICSE introduces a visual way of representing sets. This chapter of your Mathematics book shows how a closed figure stands for a set, and points inside the figure stand for its elements. You will draw diagrams for disjoint sets, overlapping sets, and sets contained inside other sets. You will also read finished diagrams to list intersections and unions. The chapter covers two sections: drawing your own diagrams, and using a given diagram.
ICSE Class 6 Mathematics Chapter 30 Venn Diagrams PDF
What is inside Chapter 30
6 pages · 2 sections · 12 worked examples · 6 exercise questions
| Section | Title |
|---|---|
| 30.1 | VENN-DIAGRAMS |
| 30.3 | USING A GIVEN VENN DIAGRAM |
- Revision Exercise (Chapter 30): 6 questions
30.1 VENN-DIAGRAMS
A Venn diagram is a closed figure with points marked inside it. The closed figure represents a set, and the points represent its elements. John Venn, an English mathematician, introduced these figures. A circle or a rectangle is most commonly used.
When you draw a Venn diagram, follow two rules. The set name goes near the boundary of the figure. Element names go near the points marked inside. Sometimes the points are omitted and only element names appear. When a set has too many elements to list, write the set’s well-defined description inside the figure. A large set such as the set of all Indians is drawn this way.
The chapter presents three relationships. For disjoint sets, draw two separate figures side by side. Disjoint sets share no elements, so A \cap B = \phi, the empty set. Conversely, if A \cap B = \phi, the sets are disjoint. For example, A = \{ 5, 10, 15 \} and B = \{ 2, 4, 6 \} share nothing.
For overlapping sets, draw two intersecting figures. Write the common elements inside the shared part. Let A be the factors of 18 and B the even numbers below 12. Then A = \{ 1, 2, 3, 6, 9, 18 \} and B = \{ 2, 4, 6, 8, 10 \}. The overlap holds \{ 2, 6 \}, so A \cap B = \{ 2, 6 \}.
When one set is contained in another, draw one circle inside the other. All parrots are birds, so the parrot circle sits inside the bird circle. The summary lists four arrangements: disjoint, overlapping, set A in set B, and all elements of B in A. The Class 6 Mathematics book page lists the other chapters in this book. The CISCE website publishes the Class 6 Mathematics syllabus.
30.3 USING A GIVEN VENN DIAGRAM
A finished Venn diagram lets you read several sets. The full set is every element inside its circle. The intersection A \cap B is the set of elements in the shared overlap. The union A \cup B is every element in either circle, written once. The count of elements in a set, written n(A), comes from counting the elements inside circle A.
Work with new letters. Let M = \{ a, b, c, d, e, f \} and N = \{ d, e, f, g, h \}. The intersection holds the shared elements: M \cap N = \{ d, e, f \}. The union lists every element from both circles once. It gives M \cup N = \{ a, b, c, d, e, f, g, h \}, which is nine elements.
A common mistake is to list the shared elements twice in the union. For M \cup N, writing d, e, f again would give twelve elements, which is wrong. Write each shared element once. The exercises also ask for n(A), n(B), n(A \cup B), and n(A \cap B). The count notation n(A) is covered in the chapter on the cardinal property of a set.
What to practise from this chapter
Work through the chapter’s single practice block to build confidence in drawing and reading Venn diagrams.
- Revision Exercise (Chapter 30) — 6 questions
Six questions make up this exercise. Questions 1 to 4 ask you to draw a Venn diagram for a given pair of sets and then read the intersection and union. Questions 5 and 6 ask you to read the same information from diagrams already drawn.
Frequently asked questions
What is a Venn diagram in Class 6 maths?
A Venn diagram is a closed figure, usually a circle or a rectangle, with points marked inside it. The closed figure represents a set, and the points represent its elements. John Venn, an English mathematician, introduced these figures for set representation.
How do you draw a Venn diagram when two sets are disjoint?
Draw two separate figures side by side, with no overlap between them. Disjoint sets share no elements, so their circles never touch. For such sets, A \cap B = \phi.
How do you find A ∪ B from a given Venn diagram without repeating elements?
List every element that appears inside either circle, and write each element only once. Elements in the overlap belong to both sets, so they appear just once in the union. Counting the listed elements gives n(A \cup B).
When do you draw one circle inside another circle in a Venn diagram?
Draw one circle inside another when all the elements of one set belong to the other set. For example, all parrots are birds, so the parrot circle sits inside the bird circle.
What does A ∩ B = φ mean?
It means the sets A and B have no element in common, so they are disjoint sets. The symbol φ stands for the empty set, which has no elements.
Reference: ICSE Class 6 Mathematics textbook material, chapter 30: Venn Diagrams — CISCE-aligned.