Question

The correct options among the following is/are

• A. If $A=\{x:x\text{is a prime number less than}2\}$, then $A$ is a singleton set
• B. If $B=\{x:x\in Z\text{and}|x-2|\le 5\}$, then $B$ is a finite set
• C. If $C=\{x:x\in Z\text{and}|x|<0\}$, then $C$ is a null set
• D. If $D=\{x:x\text{is a natural number greater than}100\}$, then $D$ is an infinite set

Answer 1

Answer: (B), (C), (D)

The correct options are
B If $B=\{x:x\in Z\text{and}|x-2|\le 5\}$, then $B$ is a finite set
C If $C=\{x:x\in Z\text{and}|x|<0\}$, then $C$ is a null set
D If $D=\{x:x\text{is a natural number greater than}100\}$, then $D$ is an infinite set

$A=\{x:x\text{is a prime number less than}2\}$
$2$ is the smallest prime number
$A=\varphi$ (null set)

$B=\{x:x\in Z\text{and}|x-2|\le 5\}$
$|x-2|\le 5$
$\Rightarrow -5\le x-2\le 5$
$\Rightarrow -3\le x\le 7$
Since, $x\in Z$
$\Rightarrow x=\{-3,-2,-1,0,1,2,3,4,5,6,7\}$
$B$ is a finite set.

$C=\{x:x\in Z\text{and}|x|<0\}$
Since, $|x|\ge 0$ (always)
So $C=\varphi$, it is a null set.

$D=\{x:x\text{is a natural number greater than}100\}$
There are infinite natural numbers greater than $100.$
$D$ is an infinite set.