Question

If $R$ is relation from $A$ to $B$, where $R=\left\{\right(x,y):x,y\in Z,x^2+y^2\le 4\}$, then the least value of $n(A\times B)$ is

• A. $25$
• B. infinite
• C. $16$
• D. $9$

Answer 1

The correct option is A $25$

$R=\left\{\right(x,y):x,y\in Z,x^2+y^2\le 4\}$
From here $x^2\ge 0,y^2\ge 0$
Now $0\le x^2\le 4,0\le y^2\le 4,x,y\in Z$
$-2\le x\le 2,-2\le y\le 2,x,y\in Z$
$\therefore$ $A=B$
and the smallest set $A$ can be $\{-2,-1,0,1,2\}$
So $n(A\times B)=25$