Which pair is not present in the smallest equivalence relation on A={1,2,3,4} containing R={(1,2),(2,3),(3,1)}?
Answer and explanation
Correct answer: (1,4)
Option D is correct. The given pairs connect 1, 2, and 3, and closure under reflexivity, symmetry, and transitivity makes them one equivalence class. Element 4 is not connected to that class, so the smallest equivalence relation contains no pair from 4 to 1, 2, or 3, including (1,4). The first three options are already given explicitly.
Frequently asked questions
What is the correct answer to this question?
(1,4)
Why is this the correct answer?
Option D is correct. The given pairs connect 1, 2, and 3, and closure under reflexivity, symmetry, and transitivity makes them one equivalence class. Element 4 is not connected to that class, so the smallest equivalence relation contains no pair from 4 to 1, 2, or 3, including (1,4). The first three options are already given explicitly.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Introduction to Relations.
