Question

If $R$ be a relation defined from $A=\{1,2,3,4\}$ to $B=\{1,3,5\},i.e.(a,b)\in R$ iff $a<b$ then $Ro{R}^{-1}$ is

• A. $\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}$
• B. $\{(3,1),(5,1)(3,2),(5,2),(5,3),(5,4)\}$
• C. $\{(3,3),(3,5),(5,3),(5,5)\}$
• D. $\{(3,3),(3,4),(4,5)\}$

Answer 1

The correct option is C $\{(3,3),(3,5),(5,3),(5,5)\}$

$R;A\in B$ under given condition $a<b$ is given by,
$R=\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}$
$R^{-1}=\{(3,1),(5,1),(3,2),(5,2),(5,3)(5,4)\}$
$Ro{R}^{-1}:$ For composing $Ro{R}^{-1}$ we will pick up an element of $R^{-1}$ first and then of $R$
$(3,1)\in R^{-1}(1,3)\in R\to (3,3)\in Ro{R}^{-1}$
$\therefore Ro{R}^{-1}=\{(3,3),(3,5),(5,3),(5,5)\}$ only.