On A = {1,2,3}, let R = {(1,1),(2,2),(3,3),(1,2),(2,1)}. Choose the correct statement.
Answer and explanation
Correct answer: R is symmetric and reflexive
For reflexivity on A, all diagonal pairs (1,1), (2,2), and (3,3) must be present; all three are listed, so R is reflexive. For symmetry, every non-diagonal pair must have its reverse. The pair (1,2) is accompanied by (2,1), and diagonal pairs reverse to themselves. Thus R satisfies both properties, making option A correct.
Frequently asked questions
What is the correct answer to this question?
R is symmetric and reflexive
Why is this the correct answer?
For reflexivity on A, all diagonal pairs (1,1), (2,2), and (3,3) must be present; all three are listed, so R is reflexive. For symmetry, every non-diagonal pair must have its reverse. The pair (1,2) is accompanied by (2,1), and diagonal pairs reverse to themselves. Thus R satisfies both properties, making option A correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Symmetric relation.
