NCERT Class 12 · Ch 1 Exercise 1.1 · Q5
NCERT Class 12 Maths · Chapter 1 Relations And Functions · Exercise 1.1 Question 5
On ℝ define aRb iff a≤b³. Check reflexivity, symmetry and transitivity.
💡 Concept Hints
- Try small positive fractions for aRa, and use explicit integer chains for 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: Neither reflexive nor symmetric nor transitive.
- For a=1/2, a³=1/8<a, so aRa fails; R is not reflexive.
- 1R2 holds since 1≤8, but 2R1 fails, disproving symmetry.
- Take a=9,b=3,c=2. Then 9≤27 and 3≤8, but 9≤8 is false; transitivity fails.
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