Class 12 Relations And Functions · Long Answer3 Markstypes_of_relations
Class 12 Maths · Relations And Functions · Long Answer #174
On R, define aRb iff a≤b. Determine the relation properties.
✅ Step-by-Step Solution
Final Answer: Reflexive and transitive, but not symmetric.
- Every real a satisfies a≤a, giving reflexivity.
- The example 1≤2 but not 2≤1 disproves symmetry.
- Whenever a≤b and b≤c, the order law gives a≤c, proving transitivity.
- Therefore R is reflexive and transitive but not symmetric; it is not an equivalence relation.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Every real a satisfies a≤a, giving reflexivity.
- [1 mark] The example 1≤2 but not 2≤1 disproves symmetry.
- [1 mark] Whenever a≤b and b≤c, the order law gives a≤c, proving transitivity.
- [0.5 marks] Therefore R is reflexive and transitive but not symmetric; it is not an equivalence relation.
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