Question

Which one of the following is a finite set?

• A. $\{x:x\in Z,x<5\}$
• B. $\{x:x\in W,x\ge 5\}$
• C. $\{x:x\in N,x>10\}$
• D. { $x:x$ is an even prime number }

Answer 1

The correct option is D { $x:x$ is an even prime number }

(A)

Let $A=\{x:x\in Z,x<5\}$

$A$ can be represented in roster form as

$A=\{........,-3,-2,..,3,4\}$ which is an infinite set

(B)

Let $B=\{x:x\in W,x\ge 5\}$

$B$ can be represented in roster form as

$B=\{5,6,7,......\}$ which is an infinite set

(C)

Let $C=\{x:x\in N,x>10\}$

$C$ can be represented in roster form as

$C=\{11,12,13,14,........\}$ which is an infinite set

(D)

Let $D=\{x:x\text{is an even prime number}\}$

The only prime number which is even is $2$

So, $D$ can be represented in roster form as

$D=\left\{2\right\}$ which is a finite set

Hence, the set in option D is a finite set.