Sets Class 6 ICSE — Cardinal Property of a Set
Sets class 6 ICSE chapter 29 is a short one — it teaches the cardinal property of a set, which is the count of its elements. This chapter defines the cardinal number, introduces the n(A) notation, and lays down the counting rules you will reuse in union and intersection work. Work through the definition and the worked examples, then practise the 13 questions of Exercise 29 to fix the ideas.
Download Cardinal Property of a Set Class 6 ICSE Mathematics Chapter 29 PDF
Download the Cardinal Property of a Set Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 3 pages, 1 sections, 13 questions.
What is inside Chapter 29
3 pages · 1 sections · 4 worked examples · 13 exercise questions
| Section | Title |
|---|---|
| 29.1 | CARDINAL NUMBER OF A SET |
- EXERCISE 29: 13 questions
29.1 CARDINAL NUMBER OF A SET
The cardinal number of a set is the number of elements it holds. For set P = \{2, 9, 11, 14\}, the cardinal number is 4, because the set contains four distinct numbers. The empty set \{ \} has no elements, so its cardinal number is 0.
The symbol for the cardinal number is the small letter n written before the set’s name. The cardinal number of set A is written n(A), and n(B) means the cardinal number of set B. For the sets above, n(P) = 4, n(M) = 3, and n(E) = 0.
Two rules govern the count. Repeated elements are counted only once, because a set never lists the same element twice. The cardinal number of an infinite set is not defined. Also watch the trap: the set \{0\} contains one element, the number zero, so n(\{0\}) = 1, while the empty set has n(\emptyset) = 0.
Worked pattern: take a set with repeats, S = \{4, 4, 9, 1, 9\}. Removing the duplicates leaves \{4, 9, 1\}, so n(S) = 3. For a word-based set, the letters of ‘PAPER’ are P, A, E, R — the repeated P counts once — so the set has 4 distinct letters.
Worked pattern: let A = \{5, 7, 8, 9\}, B = \{3, 4, 5, 6\}, and C = \{2, 4, 6, 8, 10\}. Then n(A) = 4 and n(B) = 4. The union A \cup B = \{3, 4, 5, 6, 7, 8, 9\} has 7 elements, and the intersection A \cap B = \{5\} has 1.
So n(A) + n(B) = 8 equals n(A \cup B) + n(A \cap B) = 7 + 1 = 8.
These counting rules connect to the operations on sets chapter in your maths book, where you find unions and intersections. The same idea — count each element once — carries into the work you do later with Venn diagrams.
What to practise from Sets Class 6 ICSE
Exercise 29 has 13 questions. Every question applies one of the counting rules from section 29.1. Practise these types:
- Writing cardinal numbers for sets in roster form, for the empty set, and for sets described in words, such as natural numbers between 15 and 20
- Finding n(A), n(B), n(C) and n(D) for described sets, including the letters of a word
- Finding counts of unions and intersections, such as n(A \cup B) and n(A \cap C)
- Checking the relation n(A) + n(B) = n(A \cup B) + n(A \cap B) with your own numbers
- True or false statements about the empty set, repeated elements, and equal cardinality
For each type, apply the same rule: count each distinct element once, and give the empty set a count of zero. The same convention runs through your other Class 6 ICSE books.
The Class 6 ICSE Maths hub collects the chapters of this book. The CISCE syllabus for Class 6 Mathematics is the official reference for what the exam covers.
Sets Class 6 ICSE frequently asked questions
What is the cardinal number of a set in the sets class 6 ICSE chapter?
The cardinal number of a set is the number of elements it contains. For the set A = \{2, 9, 11, 14\}, the cardinal number is 4, written n(A) = 4. The empty set has cardinal number 0.
Why do we not count repeated elements in a set?
A set never lists the same element twice. When a set appears with repeats, such as \{4, 4, 9, 1, 9\}, you count each distinct element only once, giving n = 3. The repeated values do not add to the count.
What is the cardinal number of an empty set?
The empty set has no elements, so its cardinal number is 0. Do not confuse it with the set \{0\}, which contains one element, the number zero, and has n(\{0\}) = 1.
Is n(A) + n(B) always equal to n(A ∪ B) + n(A ∩ B)?
Yes, for two finite sets. The union counts the shared elements once, and the intersection adds them back. For example, with A = \{5, 7, 8, 9\} and B = \{3, 4, 5, 6\}, both sides equal 8. This relation reappears in the Venn diagrams chapter.
Reference: ICSE Class 6 Mathematics textbook material, chapter 29: Cardinal Property of a Set — CISCE-aligned.