Class 12 Relations And Functions · Short Answer2 Markstypes_of_relations
Class 12 Maths · Relations And Functions · Short Answer #210
On R define aRb iff a−b+√2 is irrational. Test reflexivity, symmetry and transitivity.
✅ Step-by-Step Solution
Final Answer: Reflexive only.
- The diagonal value is √2 for every a, so reflexivity holds.
- For symmetry, take a=√2,b=0: the two values are 2√2 and 0. For transitivity, take a=0,b=√2/2,c=√2: the first two values are √2/2 but the composed value is 0.
- Thus R is reflexive, not symmetric and not transitive.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The diagonal value is √2 for every a, so reflexivity holds.
- [1 mark] For symmetry, take a=√2,b=0: the two values are 2√2 and 0. For transitivity, take a=0,b=√2/2,c=√2: the first two values are √2/2 but the composed value is 0.
- [0.5 marks] Thus R is reflexive, not symmetric and not transitive.
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