Relations
The relation R = {(1,1), (2,2), (3,3)} on the set A = {1, 2, 3} is
Select the correct option:
Solution
An equivalence relation
- Reflexive: Contains (1,1),(2,2),(3,3), covering all elements of A. (Yes)
- Symmetric: For every pair (a,a), the inverse is (a,a) itself, which is in R. (Yes)
- Transitive: For (a,a) and (a,a), the composite is (a,a), which is in R. No non-diagonal pairs exist to violate this. (Yes)
- Identify Identity Relation: This is specifically the 'Identity Relation' on A, which is the simplest example of an equivalence relation.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- relations
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
An equivalence relation
- Reflexive: Contains (1,1),(2,2),(3,3), covering all elements of A. (Yes)
- Symmetric: For every pair (a,a), the inverse is (a,a) itself, which is in R. (Yes)
- Transitive: For (a,a) and (a,a), the composite is (a,a), which is in R. No non-diagonal pairs exist to violate this. (Yes)
- Identify Identity Relation: This is specifically the 'Identity Relation' on A, which is the simplest example of an equivalence relation.
This easy difficulty mathematics question is from the chapter sets, relations and functions, covering the topic of relations. It appeared in the 2025 exam.
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