Mathematics - Sets and Relations Question with Solution | TestHub

$S=\{1,2,3,4,5,6\}R:S\to S$ Number of elements in $R=6$ and for each $(a,b)\in R;|a-b|\ge 2$ $X\to$ set of all relation $R:S\to S$ If $a=1,b=3,4,5,6\to (4)$ $a=2,b=4,5,6\to (3)$ $a=3,b=1,5,6\to (3)$ $a=4,b=1,2,6\to (3)$ $a=5,b=1,2,3\to (3)$ $a=6,b=1,2,3,4\to (4)$ Total number of ordered pairs $(a,b)$ s.t. $|a-b|\ge 2=20$ $\therefore n(X)=$ number of elements in $\mathrm{X}={}^{20}{C}_6$ $\therefore m=20$