NCERT Class 12 · Ch 1 Exercise 1.1 · Q4
NCERT Class 12 Maths · Chapter 1 Relations And Functions · Exercise 1.1 Question 4
On ℝ define aRb iff a≤b. Show that R is reflexive and transitive but not symmetric.
💡 Concept Hints
- Use the order properties of ≤; a strict inequality can disprove symmetry.
- 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: Reflexive and transitive, not symmetric.
- For every a∈ℝ, a≤a, so R is reflexive.
- If a≤b and b≤c, the order property of real numbers gives a≤c; hence transitive.
- For instance 1≤2 but 2≤1 is false, so R is not symmetric.
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