Class 12 Relations And Functions · Very Long Answer5 Markstypes_of_relations
Class 12 Maths · Relations And Functions · Very Long Answer #224
On R, define aRb iff a<b. Test symmetry and transitivity.
✅ Step-by-Step Solution
Final Answer: Not symmetric; transitive.
- For aRb iff a<b, symmetry would require b<a whenever a<b.
- The pair (1,2) qualifies while (2,1) does not, so R is not symmetric.
- To test transitivity, suppose aRb and bRc for arbitrary real a,b,c, so a<b and b<c.
- The strict order property gives a<c; therefore aRc and R is transitive.
- Hence R is transitive but not symmetric.
📋 CBSE Stepwise Marking Scheme
- [1 mark] For aRb iff a<b, symmetry would require b<a whenever a<b.
- [1 mark] The pair (1,2) qualifies while (2,1) does not, so R is not symmetric.
- [1 mark] To test transitivity, suppose aRb and bRc for arbitrary real a,b,c, so a<b and b<c.
- [1 mark] The strict order property gives a<c; therefore aRc and R is transitive.
- [1 mark] Hence R is transitive but not symmetric.
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