Question

Let \[{\text{A = }}\left\{ {1,2,3,4,5,6} \right\}\] . Insert the appropriate symbol $ \in $ or $ \notin $ in the blank spaces :
(i) $5...{\text{A}}$
(ii) $8...{\text{A}}$
(iii) $0...{\text{A}}$
 (iv) $4...{\text{A}}$
(v) $2...{\text{A}}$
 (vi) $10...{\text{A}}$

Answer 1

Hint: Firstly the symbol $ \in $ pronounce as belongs , in the question as some digit is given that we have to find that the digit is belongs to given set that is \[{\text{A = }}\left\{ {1,2,3,4,5,6} \right\}\] or not , If not then we insert $ \notin $ this symbol .

Complete step-by-step answer:
In this question we have to insert the following symbol $ \in $ or $ \notin $ in the following operation ,
So first we have to find what is meaning of that symbol first
$ \in $ this symbol is pronounced as belongs , in the question as some digit is given that we have to find that the digit belongs to a given set or not , If not then we insert $ \notin $ this symbol .
As in Part (i) $5...{\text{A}}$
So from here A is given set the values in A is \[{\text{A = }}\left\{ {1,2,3,4,5,6} \right\}\] and $5$ is in the set,
Hence we insert $ \in $ this symbol , $5 \in {\text{A}}$
As in Part (ii) $8...{\text{A}}$
So from here A is given set the values in A is \[{\text{A = }}\left\{ {1,2,3,4,5,6} \right\}\] and $8$ is not in the set,
Hence we insert $ \notin $ this symbol , $8 \notin {\text{A}}$
As in Part (iii) $0...{\text{A}}$
So from here A is given set the values in A is \[{\text{A = }}\left\{ {1,2,3,4,5,6} \right\}\] and $0$ is not in the set,
Hence we insert $ \notin $ this symbol , $0 \notin {\text{A}}$
As in Part (iv) $4...{\text{A}}$
So from here A is given set the values in A is \[{\text{A = }}\left\{ {1,2,3,4,5,6} \right\}\] and $4$ is in the set,
Hence we insert $ \in $ this symbol , $4 \in {\text{A}}$
As in Part (v) $2...{\text{A}}$
So from here A is given set the values in A is \[{\text{A = }}\left\{ {1,2,3,4,5,6} \right\}\] and $2$ is in the set,
Hence we insert $ \in $ this symbol , $2 \in {\text{A}}$
As in Part (vi) $10...{\text{A}}$
So from here A is given set the values in A is \[{\text{A = }}\left\{ {1,2,3,4,5,6} \right\}\] and $10$ is not in the set,
Hence we insert $ \notin $ this symbol , $10 \notin {\text{A}}$.


Note: A set is a collection of well defined objects. The objects of a set are taken as distinct only on the ground of simplicity.
A set is denoted by a capital letter and represented by listing all its elements between curly brackets such as $\left\{ {} \right\}$