Let A={1,2,3}. Which of the following relations on A is symmetric but not reflexive?
Answer and explanation
Correct answer: R={(1,2),(2,1)}
Option A is correct. A relation is symmetric when (a,b) in R always implies (b,a) in R. Here, (1,2) and (2,1) both occur, so the symmetry condition is satisfied. It is not reflexive because a reflexive relation on A must contain (1,1), (2,2), and (3,3), and none of these diagonal pairs is present. Option B is reflexive, so it does not fit. Option C is not symmetric because (1,2) is present but (2,1) is absent. Option D is both symmetric and reflexive, so it also fails the requirement of being non-reflexive.
Frequently asked questions
What is the correct answer to this question?
R={(1,2),(2,1)}
Why is this the correct answer?
Option A is correct. A relation is symmetric when (a,b) in R always implies (b,a) in R. Here, (1,2) and (2,1) both occur, so the symmetry condition is satisfied. It is not reflexive because a reflexive relation on A must contain (1,1), (2,2), and (3,3), and none of these diagonal pairs is present. Option B is reflexive, so it does not fit. Option C is not symmetric because (1,2) is present but (2,1) is absent. Option D is both symmetric and reflexive, so it also fails the requirement of being non-reflexive.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Types of relations.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
