Which pair must belong to the smallest equivalence relation on A={1,2,3,4} containing R={(1,2),(2,3),(4,4)}?
Answer and explanation
Correct answer: (1,3)
Option A is correct. In an equivalence relation, transitivity applies to (1,2) and (2,3), so (1,3) must be included. Symmetry also adds the reverse pairs, and reflexivity adds all diagonal pairs. Elements 1, 2, and 3 therefore form one equivalence class, while 4 remains separate; hence pairs joining 4 to another element are not forced.
Frequently asked questions
What is the correct answer to this question?
(1,3)
Why is this the correct answer?
Option A is correct. In an equivalence relation, transitivity applies to (1,2) and (2,3), so (1,3) must be included. Symmetry also adds the reverse pairs, and reflexivity adds all diagonal pairs. Elements 1, 2, and 3 therefore form one equivalence class, while 4 remains separate; hence pairs joining 4 to another element are not forced.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Introduction to Relations.
