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Relations and Functions
Xam Idea
CBSE
Grade 12
Question:
Show that relation $R$ in set $\mathbb{R}$ of real numbers defined as $R = \{(a, b) : a \le b^2\}$ is neither reflexive, nor symmetric, nor transitive.
Step-by-Step Solution
Key Concept: (1/2, 1/2) not in R => not refl. (1, 2) in R but (2, 1) not in R => not symm. (3, -2), (-2, -1) in R but (3, -1) not in R => not trans.
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Correct Answer:
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