Sets
ICSE Class 6 · Mathematics · Chapter 10
What this chapter covers
- The idea of a set
- Representing a set
- Finite, infinite and empty sets
- Cardinal number of a set
Key points
- A set is a well-defined collection of objects; you can always tell whether an object belongs to it.
- The objects in a set are its elements or members; in means "belongs to" and notin means "does not belong to".
- In roster form, the elements are listed inside curly brackets, each written once, in any order.
- In set-builder form, a rule describes the elements, as in \x : x is an odd number\.
- A finite set can be counted to the end; an infinite set never ends and is shown with three dots.
- The empty set has no elements and is written as \ \ or φ; the set \0\ is not empty.
- The cardinal number n(A) is the number of different elements in a finite set A, and n(φ) = 0.
Questions answered
Which of these collections are sets? (a) the colours of the Indian national flag (b) the clever students of your school (c) the prime numbers less than 10
(a) and (c) are sets, because everyone agrees on their members. (b) is not a set, because "clever" is not well-defined.
A = \2, 3, 5, 7\. Fill in in or notin: 5 ___ A, 9 ___ A.
5 in A and 9 notin A.
Write in roster form: the set of letters in the word "SCHOOL".
\S, C, H, O, L\. The letter O is written only once.
Write in set-builder form: \1, 4, 9, 16, 25\.
\x : x is the square of a natural number from 1 to 5\. Any rule giving exactly these five numbers is correct.
Write in roster form: \x : x is a multiple of 3 between 10 and 25\.
\12, 15, 18, 21, 24\.
Say whether each set is finite, infinite or empty. (a) the set of natural numbers greater than 100 (b) the set of months beginning with the letter J (c) the set of even numbers between 6 and 8
(a) infinite (b) finite: January, June and July (c) empty, as 7 is the only number between 6 and 8 and it is odd.
Is \0\ the empty set? Give a reason.
No. The set \0\ has one element, the number 0. The empty set has no elements.
Find the cardinal number: (a) \x : x is a letter of the word COCONUT\ (b) \x : x is a natural number less than 1\
(a) The different letters are C, O, N, U and T, so the cardinal number is 5. (b) The set is empty, so the cardinal number is 0.