NCERT Class 12 · Ch 1 Exercise 1.1 · Q6
NCERT Class 12 Maths · Chapter 1 Relations And Functions · Exercise 1.1 Question 6
On A={1,2,3}, R={(1,2),(2,1)}. Show that it is symmetric but neither reflexive nor transitive.
💡 Concept Hints
- A two-step chain can return to its starting point.
- Work through the definitions using the stated domain and codomain; justify a failed universal property with one valid counterexample.
✅ Step-by-Step Solution
Final Answer: Symmetric only.
- Both non-diagonal pairs have their reverses in R, so it is symmetric.
- (1,1) is absent, so it is not reflexive on A.
- (1,2),(2,1) are in R but (1,1) is absent, so it is not transitive.
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