Question

Which of the following sets is not a finite set ?

• A. $\left\{\right(x,y):x^2+y^2\le 1\le x+y,x,y\in R\}$
• B. $\left\{\right(x,y):x^2+y^2\le 1\le x+y,x,y\in Z\}$
• C. $\left\{\right(x,y):x^2\le y\le |x|,x,y\in Z\}$
• D. $\left\{\right(x,y):x^2+y^2=1,x,y\in Z\}$

Answer 1

The correct option is A $\left\{\right(x,y):x^2+y^2\le 1\le x+y,x,y\in R\}$

The set $\left\{\right(x,y):x^2+y^2\le 1\le x+y,x,y\in R\}$ consists of all the points in the first quadrant which lie inside the circle $x^2+y^2=1$ and above the line $x+y=1$ .So, it is not a finite set.
Option $A$ is correct.