NCERT Class 12 · Ch 1 Exercise 1.1 · Q15
NCERT Class 12 Maths · Chapter 1 Relations And Functions · Exercise 1.1 Question 15
On A={1,2,3,4}, let R={(1,2),(2,2),(1,1),(4,4),(1,3),(3,3),(3,2)}. Choose the correct property description.
💡 Concept Hints
- Check the nontrivial chain through 3 after checking diagonal and reverse pairs.
- 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: B.
- All four diagonal pairs occur, so R is reflexive.
- (1,2) occurs but (2,1) does not, so R is not symmetric.
- Diagonal compositions add nothing. The only nontrivial chain with distinct intermediate progress is 1R3R2, whose shortcut (1,2) is present. Thus R is transitive.
- Select B: reflexive and transitive but not symmetric.
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