Question

If $A=\{y:x^2+y^2<1,x\in N\}$ and $B=\{y:x^2+y^2=4,x\in N\},$ then $n(A\times B)$ is

• A. $0$
• B. $1$
• C. $3$
• D. infinite

Answer 1

The correct option is A $0$

$A=\{y:x^2+y^2<1,x\in N\}$
We know that,
$y^2\ge 0,x^2\ge 1\Rightarrow x^2+y^2\ge 1\Rightarrow A=\left\{\right\}=\varphi$

$B=\{y:x^2+y^2=4,x\in N\}{y}^2\ge 0,x^2\ge 1\Rightarrow B=\{-\sqrt{3},0,\sqrt{3}\}$
$\therefore n(A\times B)=0$