1.3 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 \(\phi\).

Given below are few examples of empty sets.
(i) Let \(\mathrm{A}=\{x: 1<x<2, x\) is a natural number \(\}\). Then \(\mathrm{A}\) is the empty set, because there is no natural number between 1 and 2 .
(ii) \(\mathrm{D}=\left\{x: x^{2}=4, x\right.\) is odd \(\}\). Then \(\mathrm{D}\) is the empty set, because the equation \(x^{2}=4\) is not satisfied by any odd value of \(x\).

Examples: Find Null Set from the given cases

\(A=\{x: x \in N \text { and }(\underbrace{x-1)(x-2)=0\}}_{\substack{x=1 \\ x=2}} \Rightarrow A=\{1,2\}, \text { Set A is not a null set. } \\\) \(B=\{x: x \in N \text { and }{\left.x^2=4\right\}}\Rightarrow B=\{2\}, \text { Set B is not a null set. } \\\)

\(C=\{x:(x \in N \text { and } 2 x-1=0\} \quad \Rightarrow \quad C=\{\quad\}, \text { Set C is a null set. }\)