# Elements of a Set

What are the elements of a set or members of a set?

The objects used to form a set are called its element or its members.

Generally, the elements of a set are written inside a pair of curly (idle) braces and are represented by commas. The name of the set is always written in capital letter.

Solved Examples to find the elements or members of a set:

1. A = {v, w, x, y, z}

Here ‘A’ is the name of the set whose elements (members) are v, w, x, y, z.

2. If a set A = {3, 6, 9, 10, 13, 18}. State whether the following statements are ‘true’ or ‘false’:

(i) 7 ∈ A

(ii) 12 ∉ A

(iii) 13 ∈ A

(iv) 9, 12 ∈ A

(v) 12, 14, 15 ∈ A

Solution:

(i) 7 ∈ A

False, since the element 7 does not belongs to the given set A.

(ii) 10 ∉ A

False, since the element 10 belongs to the given set A.

(iii) 13 ∈ A

True, since the element 13 belongs to the given set A.

(iv) 9, 10 ∈ A

True, since the elements 9 and 12 both belong to the given set A.

(v) 10, 13, 14 ∈ A

False, since the element 14 does not belongs to the given set A.

3. If set Z = {4, 6, 8, 10, 12, 14}. State which of the following statements are ‘correct’ and which are ‘wrong’ along with the correct explanations

(i) 5 ∈ Z

(ii) 12 ∈ Z

(iii) 14 ∈ Z

(iv) 9 ∈ Z

(v) Z is a set of even numbers between 2 and 16.

(vi) 4, 6 and 10 are members of the set Z.

Solution:

(i) 5 ∈ Z

Wrong, since 5 does not belongs to the given set Z i.e. 5 ∉ Z

(ii) 12 ∈ Z

Correct, since 12 belongs to the given set Z.

(iii) 14 ∈ Z

Correct, since 14 belongs to the given set Z.

(iv) 9 ∈ Z

Wrong, since 9 does not belongs to the given set Z i.e. 9 ∉ Z

(v) Z is a set of even numbers between 2 and 16.

Correct, since the elements of the set Z consists of all the multiples of 2 between 2 and 16.

(vi) 4, 6 and 10 are members of the set Z.

Correct, since the 4, 6 and 10 those numbers belongs to the given set Z.

Set Theory

Sets

Objects Form a Set

Elements of a Set

Properties of Sets

Representation of a Set

Different Notations in Sets

Standard Sets of Numbers

Types of Sets

Pairs of Sets

Subset

Subsets of a Given Set

Operations on Sets

Union of Sets

Intersection of Sets

Difference of two Sets

Complement of a Set

Cardinal number of a set

Cardinal Properties of Sets

Venn Diagrams