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
● Subset
7th Grade Math Problems
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