Class 12 Relations And Functions · Long Answer3 Markstypes_of_relations
Class 12 Maths · Relations And Functions · Long Answer #214
On N×N define (a,b)R(c,d) iff a²+d²=b²+c². Prove equivalence.
✅ Step-by-Step Solution
Final Answer: An equivalence relation.
- Rewrite the condition as a²−b²=c²−d². Each pair has the same squared difference as itself, proving reflexivity.
- Equality of the squared differences is symmetric, so (a,b)R(c,d) implies (c,d)R(a,b).
- If a²−b²=c²−d² and c²−d²=e²−f², then a²−b²=e²−f², proving transitivity.
- All three properties hold; R is an equivalence relation.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Rewrite the condition as a²−b²=c²−d². Each pair has the same squared difference as itself, proving reflexivity.
- [1 mark] Equality of the squared differences is symmetric, so (a,b)R(c,d) implies (c,d)R(a,b).
- [1 mark] If a²−b²=c²−d² and c²−d²=e²−f², then a²−b²=e²−f², proving transitivity.
- [0.5 marks] All three properties hold; R is an equivalence relation.
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