What is the smallest change needed to make R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)} an equivalence relation on A={1,2,3}?
Answer and explanation
Correct answer: Add (1,3) and (3,1)
Option A is correct. The relation already contains every diagonal pair, so it is reflexive, and every listed off-diagonal pair has its reverse, so it is symmetric. Transitivity requires (1,3) from (1,2) and (2,3), and symmetry then requires (3,1). After adding both, all pairs of A×A are present, making the relation an equivalence relation.
Frequently asked questions
What is the correct answer to this question?
Add (1,3) and (3,1)
Why is this the correct answer?
Option A is correct. The relation already contains every diagonal pair, so it is reflexive, and every listed off-diagonal pair has its reverse, so it is symmetric. Transitivity requires (1,3) from (1,2) and (2,3), and symmetry then requires (3,1). After adding both, all pairs of A×A are present, making the relation an equivalence relation.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Introduction to Relations.
