Question

Show that the relation R in the set R of real numbers defined as $R=\left\{\right(a,b):a\le b^2\}$ is neither reflexive nor symmetric nor transitive.

Answer 1

$\Rightarrow a\le a^2\text{is not true}\Rightarrow \text{R is not reflexive}\text{If a = 2, b = 9}\Rightarrow a\le b^2\text{but}b>a^2\Rightarrow (a,b)ϵR\text{but}(b,a)\notin R\Rightarrow \text{R is not symmetric}\text{a = 4, b = – 3, c = 1}\Rightarrow a\le b^2\text{and}b\le c^2\text{but}a>c^2\Rightarrow \text{R is not transitive}$