For R={(1,1),(2,2),(3,3),(2,3),(3,2)} on A={1,2,3}, which property does R fail to satisfy?
Answer and explanation
Correct answer: Antisymmetry
All three diagonal pairs are present, so R is reflexive. The non-diagonal pair (2,3) appears together with (3,2), so symmetry also holds. However, antisymmetry requires that if both (a,b) and (b,a) occur, then a=b. Here both pairs occur although 2≠3, so R is not antisymmetric. Every listed ordered pair still belongs to A×A.
Frequently asked questions
What is the correct answer to this question?
Antisymmetry
Why is this the correct answer?
All three diagonal pairs are present, so R is reflexive. The non-diagonal pair (2,3) appears together with (3,2), so symmetry also holds. However, antisymmetry requires that if both (a,b) and (b,a) occur, then a=b. Here both pairs occur although 2≠3, so R is not antisymmetric. Every listed ordered pair still belongs to A×A.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Introduction to Relations.
