Mathematics - Sets and Relations Question with Solution | TestHub

$\begin{array}{rl}& A=\{1,2,3\}\\ & (1,1),(2,2),(3,3),(1,2)\in R\end{array}$
Remaining elements are
$(2,1),(2,3),(1,3),(3,1),(3,2)$
(1) If relation contains exactly 4 elements = 1 way
(2) if relation contains exactly 5 elements
It can be $(1,3),(3,2)\Rightarrow 2$ ways
(3) If relation contain exactly 6 elements
It can be $((2,3),(1,3)),((1,3),(3,2)),((3,1),(3,2))$
$\Rightarrow 3$ ways.
Total $=6$ ways