CUET · MATHS · PYQ PAPER 2025
The relation R on the set of real numbers defined by \(R=\left\{(a, b): a \leq b^2\right\}\) is
(A) Reflexive
(B) Not symmetric
(C) Neither reflexive nor transitive
(D) Transitive
Choose the correct answer from the options given below:
- A (A) and (D) only
- B (A), (B) and (D) only
- C (B) and (C) only
- D (A) and (C) only
Answer & Solution
Correct Answer
(C) (B) and (C) only
Step-by-step Solution
Detailed explanation
Reflexivity: \(a \leq a^2\). Let \(a=0.5\). \(0.5 \leq (0.5)^2 \implies 0.5 \leq 0.25\). False. Not reflexive. Symmetry: If \((a,b) \in R\), then \((b,a) \in R\). Let \((a,b)=(1,2)\). \(1 \leq 2^2\). True. Check \((2,1)\): \(2 \leq 1^2 \implies 2 \leq 1\). False. Not symmetric.…
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