Browse Questions

# If $S$ is a set having 10 elements in it and $A$ is a relation in $S$ defined as $A=\{(x,y)$, where $x,y \in\:S\;$ and $\;x\neq\;y.\}$, then no. of elements in $A$ is

$\begin{array}{1 1} 45 \\ 50 \\ 90 \\ 100 \end{array}$

Toolbox:
• A relation in any set S is a sub set of $S\times\:S$.
• If no. of elements in $S= n(S)=n$, then $n(S\times\:S)=n^2$
Ans: ( C) 90
Given $n(S)=10 \:\:\Rightarrow\: n(S\times\:S)=100$
But $A\subset(S\times\:S)$
But A does not have elements $(x,x)$ which are 10 in number.
$\Rightarrow$ no. of elements in A =100-10 =90