NCERT Class 12 · Ch 1 Exercise 1.1 · Q3
NCERT Class 12 Maths · Chapter 1 Relations And Functions · Exercise 1.1 Question 3
On {1,2,3,4,5,6}, define aRb iff b=a+1. Check reflexivity, symmetry and transitivity.
💡 Concept Hints
- List the ordered pairs; then test a diagonal, a reverse and a two-step chain.
- 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: Neither reflexive nor symmetric nor transitive.
- The relation is {(1,2),(2,3),(3,4),(4,5),(5,6)}.
- No (a,a) belongs, so reflexivity fails.
- (1,2) belongs but (2,1) does not, so symmetry fails.
- (1,2),(2,3) belong but (1,3) does not, so transitivity fails.
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