Class 12 Relations And Functions · Long Answer3 Markstypes_of_relations
Class 12 Maths · Relations And Functions · Long Answer #216
On A={1,…,12}, define aRb iff 3 divides a−b. Prove equivalence and find [1].
✅ Step-by-Step Solution
Final Answer: Equivalence; [1]={1,4,7,10}.
- The diagonal differences are 0, so reflexivity holds.
- If a−b=3k, then b−a=3(−k), proving symmetry. If also b−c=3l, then a−c=3(k+l), proving transitivity.
- The condition 3|(x−1) with x∈A gives x=1,4,7,10.
- Thus R is an equivalence relation and [1]={1,4,7,10}.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The diagonal differences are 0, so reflexivity holds.
- [1 mark] If a−b=3k, then b−a=3(−k), proving symmetry. If also b−c=3l, then a−c=3(k+l), proving transitivity.
- [1 mark] The condition 3|(x−1) with x∈A gives x=1,4,7,10.
- [0.5 marks] Thus R is an equivalence relation and [1]={1,4,7,10}.
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