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

7th Grade Math Problems

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