Class 12 Relations And Functions · Short Answer2 Markstypes_of_relations
Class 12 Maths · Relations And Functions · Short Answer #163
On R, define aRb iff a<b. Test symmetry and transitivity.
✅ Step-by-Step Solution
Final Answer: Not symmetric; transitive.
- Symmetry would require b<a whenever a<b; transitivity requires a<c whenever a<b and b<c.
- 1<2 but 2<1 is false, so symmetry fails. The order law a<b<c implies a<c, so transitivity holds.
- Therefore R is transitive but not symmetric.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Symmetry would require b<a whenever a<b; transitivity requires a<c whenever a<b and b<c.
- [1 mark] 1<2 but 2<1 is false, so symmetry fails. The order law a<b<c implies a<c, so transitivity holds.
- [0.5 marks] Therefore R is transitive but not symmetric.
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