Class 12 Relations And Functions · Long Answer3 Markstypes_of_relations
Class 12 Maths · Relations And Functions · Long Answer #215
On R, let aRb iff a≤b³. Test reflexivity, symmetry and transitivity.
✅ Step-by-Step Solution
Final Answer: None of the three properties holds.
- The predicate is a≤b³; at a=1/3 the diagonal inequality fails.
- Symmetry fails since 1R2 holds but 2R1 does not.
- Transitivity fails: 10R3 and 3R2 hold, but 10R2 does not.
- Hence the relation is neither reflexive, symmetric nor transitive.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The predicate is a≤b³; at a=1/3 the diagonal inequality fails.
- [1 mark] Symmetry fails since 1R2 holds but 2R1 does not.
- [1 mark] Transitivity fails: 10R3 and 3R2 hold, but 10R2 does not.
- [0.5 marks] Hence the relation is neither reflexive, symmetric nor transitive.
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