the relation R in the set R of real numbers, defined as $R=\left\{(a,b):a\le b^2\right\}$  is 

Given $R=\left\{(a,b):a\le b^2\right\}$

For $\left(\frac{1}{2},\frac{1}{2}\right)\notin R as \frac{1}{2}>{\left(\frac{1}{2}\right)}^2$

Therefore, R is not reflexive

$\text{ Now, }(1,4)\in R\text{ as }1<4^2$

$\text{ But, }4\text{ is not less than }1\text{ . }$

$\text{ Therefore, }(4,1)\notin R$

$\text{ Therefore, }R\text{ is not symmetric, }$

$\text{ Now, }(3,2),(2,1.5)\in \mathrm{R}\text{ (as }3<2^2=4\text{ and }2<(1.5{)}^2=2.25\text{ ) }$

$\text{ But, }3>(1.5{)}^2=2.25$

$\text{ Therefore, }(3,1.5)\notin R$

Therefore, R is not transitive. Hence, R is neither reflexive, nor symmetric, nor transitive