Class 12 Relations And Functions · Long Answer3 Markstypes_of_relations
Class 12 Maths · Relations And Functions · Long Answer #218
On Z define aRb iff a−b is divisible by 5. Prove equivalence.
✅ Step-by-Step Solution
Final Answer: An equivalence relation.
- Since a−a=0=5·0, R is reflexive.
- If a−b=5k, then b−a=5(−k), proving symmetry.
- If a−b=5k and b−c=5l, then a−c=5(k+l), proving transitivity.
- Therefore R is an equivalence relation on Z.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Since a−a=0=5·0, R is reflexive.
- [1 mark] If a−b=5k, then b−a=5(−k), proving symmetry.
- [1 mark] If a−b=5k and b−c=5l, then a−c=5(k+l), proving transitivity.
- [0.5 marks] Therefore R is an equivalence relation on Z.
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