Question

The given relation is defined on the set of real numbers check them for Reflexive,Symmetric,Transitive.

$\left|a\right|\le b.$

Answer 1

$\left|a\right|\le b\ne R.$ Choose $a=-3$ any real number

$\left|a\right|=|-3|=3$ but 3 is not less than or equal to -3

$\therefore$ a is not related to a.

$\ne S,a=-2,b=3$

$\left|a\right|=2<b=3$ but $\left|b\right|=3$ which is not less than or qual to a i.e. -2.

$\therefore$ aRb does not imply bRa.

T $aRb\Rightarrow \left|a\right|\le b.$ ...(1)

Since $\left|a\right|$ is +ive $\therefore$ b is certainly +ive.

$bRc\Rightarrow \left|b\right|\le c\therefore \left|a\right|\le c.$ Hence aRc.