Class 12 Relations And Functions · Short Answer2 Markstypes_of_relations
Class 12 Maths · Relations And Functions · Short Answer #208
For A={1,2,3,4,5}, list R={(a,b)∈A²:|a²−b²|<8}.
✅ Step-by-Step Solution
Final Answer: {(1,1),(2,2),(3,3),(4,4),(5,5),(1,2),(2,1),(2,3),(3,2),(3,4),(4,3)}.
- Every diagonal pair qualifies because its squared difference is 0.
- The qualifying unordered off-diagonal pairs are {1,2},{2,3},{3,4}, with squared differences 3,5,7. All others have difference at least 8; include both directions for each qualifying pair.
- Thus R consists of the five diagonal pairs and (1,2),(2,1),(2,3),(3,2),(3,4),(4,3), giving 11 pairs.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Every diagonal pair qualifies because its squared difference is 0.
- [1 mark] The qualifying unordered off-diagonal pairs are {1,2},{2,3},{3,4}, with squared differences 3,5,7. All others have difference at least 8; include both directions for each qualifying pair.
- [0.5 marks] Thus R consists of the five diagonal pairs and (1,2),(2,1),(2,3),(3,2),(3,4),(4,3), giving 11 pairs.
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