The relation $R$ in $\mathbb{R}$ defined by $R = \{(a, b) : a \le b^2\}$ is:
(a) Neither reflexive, nor symmetric, nor transitive
(b) Reflexive only
(c) Transitive only
(d) Equivalence relation
Step-by-Step Solution
Key Concept: (1/2, 1/2) not in R => not reflexive. (1,2) in R but (2,1) not in R. (2,-2) & (-2,1) in R but (2,1) not in R.
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Correct Answer: Neither reflexive, nor symmetric, nor transitive