Which single pair should be added to R={(1,1),(2,2),(3,3),(1,2)} so that it becomes an equivalence relation on A={1,2,3}?
Answer and explanation
Correct answer: (2,1)
Option A is correct. The relation already contains all diagonal pairs, so it is reflexive. To make the elements 1 and 2 belong to the same equivalence class, symmetry requires the reverse pair (2,1). After adding it, the classes are {1,2} and {3}; transitivity is satisfied within each class, and no pair involving 3 needs to be added.
Frequently asked questions
What is the correct answer to this question?
(2,1)
Why is this the correct answer?
Option A is correct. The relation already contains all diagonal pairs, so it is reflexive. To make the elements 1 and 2 belong to the same equivalence class, symmetry requires the reverse pair (2,1). After adding it, the classes are {1,2} and {3}; transitivity is satisfied within each class, and no pair involving 3 needs to be added.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Types of relations.
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