Class 12 Relations And Functions · Very Long Answer5 Markstypes_of_relations
Class 12 Maths · Relations And Functions · Very Long Answer #223
On N, define aRb iff a divides b. Determine whether it is an equivalence relation.
✅ Step-by-Step Solution
Final Answer: Reflexive and transitive, not symmetric; not an equivalence relation.
- On positive integers aRb means b=ak for an integer k.
- Reflexivity holds since a=a·1 for every a.
- Symmetry fails: 2 divides 6 but 6 does not divide 2.
- If b=ak and c=bl, then c=a(kl), so a divides c and transitivity holds.
- Thus the relation is reflexive and transitive but not symmetric, and is not an equivalence relation.
📋 CBSE Stepwise Marking Scheme
- [1 mark] On positive integers aRb means b=ak for an integer k.
- [1 mark] Reflexivity holds since a=a·1 for every a.
- [1 mark] Symmetry fails: 2 divides 6 but 6 does not divide 2.
- [1 mark] If b=ak and c=bl, then c=a(kl), so a divides c and transitivity holds.
- [1 mark] Thus the relation is reflexive and transitive but not symmetric, and is not an equivalence relation.
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