NCERT Class 12 · Ch 1 Exercise 1.1 · Q2
NCERT Class 12 Maths · Chapter 1 Relations And Functions · Exercise 1.1 Question 2
On ℝ define aRb iff a≤b². Show that R is neither reflexive nor symmetric nor transitive.
💡 Concept Hints
- Try a number between 0 and 1 for reflexivity; negative middle values can help test transitivity.
- Work through the definitions using the stated domain and codomain; justify a failed universal property with one valid counterexample.
✅ Step-by-Step Solution
Final Answer: None of the three properties holds.
- Reflexivity fails at a=1/2 because 1/2≤1/4 is false.
- Symmetry fails: 1R2 since 1≤4, but 2R1 is false since 2≤1 is false.
- Transitivity fails: 2R(−2) and (−2)R1 are true, but 2R1 is false.
- Each counterexample lies in ℝ, so the three universal properties are disproved.
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