if B={0,4,8,12,16,20,24} and C={0,5,10,15,20,25}, then cardinal mumber of b intersecrion c is options is 2 and 4
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1.1 Overview
This chapter deals with the concept of a set, operations on sets.Concept of sets will be
useful in studying the relations and functions.
1.1.1 Set and their representations A set is a well-defined collection of objects.
There are two methods of representing a set
(i) Roaster or tabular form (ii) Set builder form
1.1.2 The empty set A set which does not contain any element is called the empty
set or the void set or null set and is denoted by { } or φ.
1.1.3 Finite and infinite sets A set which consists of a finite number of elements is
called a finite set otherwise, the set is called an infinite set.
1.1.4 Subsets A set A is said to be a subset of set B if every element of A is also an
element of B. In symbols we write A ⊂ B if a ∈ A ⇒ a ∈ B.
We denote set of real numbers by R
set of natural numbers by N
set of integers by Z
set of rational numbers by Q
set of irrational numbers by T
We observe that
N ⊂ Z ⊂ Q ⊂ R,
T ⊂ R, Q ⊄ T, N ⊄ T
1.1.5 Equal sets Given two sets A and B, if every elements of A is also an element of
B and if every element of B is also an element of A, then the sets A and B are said to
be equal. The two equal sets will have exactly the same elements.
1.1.6 Intervals as subsets of R Let a, b ∈ R and a < b. Then
(a) An open interval denoted by (a, b) is the set of real numbers {x : a < x < b}
(b) A closed interval denoted by [a, b] is the set of real numbers {x : a ≤ x ≤ b)
Chapter 1
SETS
18/04/18
2 EXEMPLAR PROBLEMS – MATHEMATICS
(c) Intervals closed at one end and open at the other are given by
[a, b) = {x : a ≤ x < b}
(a, b] = {x : a < x ≤ b}