In this post we will learn about elements or objects of sets with solved examples.

**What are set elements?**

The **objects or members present inside the set** is called **set elements**.

**Set elements are present inside the curly bracket **that represent any particular set.

**Examples of set elements**

**(i) E = { 2, 4, 6, 8, 10 }**

Here;

E is the set name.

2, 4, 6, 8 and 10 are the set elements.

**(ii) Y = { “Red”, “Orange”, “Yellow”, “Green”}**

Here,

Y is the set name.

Red, Orange, Yellow and Green are the set elements.

**(iii) A = { -3, 0, 9, 15}**

Here A is the set name.

-3, 0, 9 and 5 are the set elements.

**Representing set elements**

We use the symbol epsilon ” \mathtt{\ \epsilon \ } ” to show that the given element is the part of the set.

For Example, consider the below set.

X = { 9, 19, 25, 30 }

Here;

X is the name of the set.

9, 19, 25 and 30 are the elements of set.

We can say that;

9 \mathtt{\ \epsilon \ } X, It means element 9 belongs to X.

Similarly we can write this for all the elements of X.

19 \mathtt{\ \epsilon \ } X ;

25 \mathtt{\ \epsilon \ } X ;

30 \mathtt{\ \epsilon \ } X ;

Remember the significance of above symbol as it is directly asked in the examinations.

**What does symbol** \mathtt{\notin } **mean in set theory?**

The symbol \mathtt{\notin } represents that the element doesn’t belongs to a particular set.

For Example, consider the below set.

X = { 5, 19, 25, 54}

We know that number 60 doesn’t belongs to the set X.

This statement can be expressed as: 60 \mathtt{\notin } X.

**What is size of a set?**

The **number of elements present in a given set** is known as **size of a set**.

For Example, consider the below set;

A = { 19, 23, 51, 64, 71 }

Note that there are 5 elements in the set; 19, 23, 51, 64 and 71.

Hence, the size of the set is 5.

Similarly, consider the below set Y’

Y = { 2, 4, 6, 8, 10, 12 . . . . . 2n}

Here Y is the never ending set of even numbers.

The number of elements in set Y is infinite.

Hence, the size of set is also infinite.

**Solved examples of elements of Set**

**(01) Given below is the set A.**

A = { 99, -33, 21, 15, -73, 21 }

List down all the elements/members of the set.

**Solution**

The elements are set are: 99, -33, 21, 15, -73 and 21.

**(02) List down all the elements of the below set X**

X = { A, P, L, E }

**Solution**

The elements of the set are: A, P, L, E

**(03)** Given below are statements regarding set A. Check is the statement is True or False.

**A = { -2, 6, -5, 10, -15, 20 }**

(i) 6 \mathtt{\ \epsilon \ } A

(ii) 5 \mathtt{\ \epsilon \ } A

(iii) 20 \mathtt{\ \epsilon \ } A

(iv) -15 \mathtt{\ \epsilon \ } A

(v) 7 \mathtt{\ \epsilon \ } A

**Solution**

(i) 6 \mathtt{\ \epsilon \ } A

The statement is correct as 6 is an element of set A.

(ii) 5 \mathtt{\ \epsilon \ } A

The statement is incorrect as 5 is not an element of A.

(iii) 20 \mathtt{\ \epsilon \ } A

It’s a correct statement as element 20 belongs to set A.

(iv) -15 \mathtt{\ \epsilon \ } A

It’s a correct statement.

(v) 7 \mathtt{\ \epsilon \ } A

This statement is False.

**(04) Given below is the set Y.**

Y = { \mathtt{\frac{1}{2} ,\ \frac{1}{6} ,\ \frac{1}{18} ,\ \frac{1}{36}} }

Check if the below statements are correct or not.

(i) \mathtt{\frac{1}{2} \ \notin \ Y}

(ii) \mathtt{\frac{1}{3} \ \epsilon \ Y}

(iii) \mathtt{\frac{1}{18} \ \epsilon \ Y}

(iv) \mathtt{\frac{1}{7} \ \notin \ Y}

(v) \mathtt{\frac{1}{36} \ \epsilon \ Y}

**Solution**

(i) \mathtt{\frac{1}{2} \ \notin \ Y}

This is incorrect statement.

1/2 is an elements belongs to set A.

So the correct expression is; \mathtt{\frac{1}{2} \ \epsilon \ Y}

(ii) \mathtt{\frac{1}{3} \ \epsilon \ Y}

This is an incorrect statement.

1/3 is not the member of set Y.

(iii) \mathtt{\frac{1}{18} \ \epsilon \ Y} .

This is a correct expression.

Element 1/3 belongs to set Y.

(iv) \mathtt{\frac{1}{7} \ \notin \ Y}

This is a correct expression.

1/7 is not part of set Y.

(v) \mathtt{\frac{1}{36} \ \epsilon \ Y}

This is correct statement.

Element 1/36 belongs to set Y.

**(05) Find the size of the below sets.**

(i) A = { 2, 9, -13, 7, 13}

(ii) B = { 23, 19, 7 }

(iii) X = { A, M, U, V }

(iv) Y = { 0 }

(v) Z = { }

**Solution**

(i) A = { 2, 9, -13, 7, 13}

There are 5 elements in the given set, namely 2, 9, -13, 7, 13.

Hence, the size of set is 5.

(ii) B = { 23, 19, 7 }

There are 3 elements in the set.

Hence, the size of set is 3.

(iii) X = { A, M, U, V }

There are 4 elements in set, namely A, M, U , V.

Hence, the size of set is 4.

(iv) Y = { 0 }

There is only one element in set, namely 0

Hence, the size of set is 1.

(v) Z = { }

There is no element is set Z.

Hence, it is a null set.