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CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/3 · Q252 Marksrelation_properties

CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/3 · Question 25 (Relations And Functions)

Thumb pins on a graph sheet are related when their distance is less than 3 cm. Determine whether this defines an equivalence relation.

✅ Step-by-Step Solution

Final Answer: Reflexive and symmetric; transitivity is not guaranteed.
  1. Every point is distance zero from itself, and distances are symmetric.
  2. Three pins at (0,0),(2,0),(4,0) cm give two successive distances below 3 but an end-to-end distance of 4.
  3. Thus the rule is not an equivalence relation in general. For a particular pin arrangement transitivity depends on that arrangement.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Every point is distance zero from itself, and distances are symmetric.
  • [1 mark] Three pins at (0,0),(2,0),(4,0) cm give two successive distances below 3 but an end-to-end distance of 4.
  • [0.5 marks] Thus the rule is not an equivalence relation in general. For a particular pin arrangement transitivity depends on that arrangement.

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