Question

Show that the relation $R$ in $R$ (Set of real numbers) is defined as $R=\{(a,b):a\le b\}$ is relexive and transitive but not symmetric.

Answer 1

$\forall a\in R(a,a)\in R$
$\therefore$ $R$ is reflexive
as $(1,2)\in R$ but $(2,1)\notin R$
$\therefore$ $R$ is not symmetric
as $(a,b)\in R;(b,c)\notin R$
$\therefore$ $R$ is transitive