Class 12 Relations And Functions · Long Answer3 Markstypes_of_relations
Class 12 Maths · Relations And Functions · Long Answer #175
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.
- For each positive integer a, a=a·1, so a divides itself.
- Symmetry fails because 2 divides 6 but 6 does not divide 2.
- If b=ak and c=bl for integers k,l, then c=a(kl), so a divides c.
- Thus R is reflexive and transitive but not symmetric, and cannot be an equivalence relation.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] For each positive integer a, a=a·1, so a divides itself.
- [1 mark] Symmetry fails because 2 divides 6 but 6 does not divide 2.
- [1 mark] If b=ak and c=bl for integers k,l, then c=a(kl), so a divides c.
- [0.5 marks] Thus R is reflexive and transitive but not symmetric, and cannot be an equivalence relation.
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