Null Set Definition

A set is a collection of well defined objects. What do we mean by well defined objects? What is your favourite subject? Your answer may be math, science or history or geography. If you ask the same question to your friend, then she may say commerce. The answer differs from person to person. It is not well defined. If you ask the following question “Name the days in a week?” to anyone, then the answer will be universally same. It is well defined.

Introduction to Null Set Definition:

Consider the following sets.

The set of vowels in English alphabet = {a, e, i, o, u} --- 1

Set of numbers divisible by 2 = {2, 4, 6, 8, 10…} --- 2

The number of elements in a set is called cardinal number of the set. If A = {a, e, i, o, u}, then cardinal number of set A, denoted as n (A) = 5.

If we could write the cardinal number of the set then it is called finite set. Set 1 is a finite set. We could not count the number of elements in set 2. So it is called as infinite set.

Definition of null set:

A null set is a set whose cardinal number is zero. In other words, a null set is a set which has no elements. Null set is also called as empty set or void set. The empty set is denoted by the symbol {} or φ

Problems on Null Set:

Ex :   Let A = {x: 2< x <3, x is a whole number}. Then A is the empty set, because there is no natural number between 2 and 3.

Sol : Let B = {x: x² – 5 = 0 and x is a natural number}. Then B is an empty set because the equation x² – 5 = 0 is not satisfied by ant rational value of x.

Let C = {x: x² = 25, x is even}. Then C is an empty set, because the equation x² = 25 is not satisfied by any even value of x.