Question

The correct options among the following is/are

• A. The set of even prime numbers greater than $2$ is a null set
• B. The set of all good soccer players is a finite set
• C. $A=\{x:x^2-3x+2=0\}$ and $B=\{x,x\in N\text{and}|x|\le 2\},$ then they are equal sets.
• D. Set of number which are factors of $8$ and set of number which are factors of $10$ are equal sets.

Answer 1

Answer: (A), (C)

$A=\{x:x^2-3x+2=0\}$ and $B=\{x,x\in N\text{and}|x|\le 2\},$ then they are equal sets.

There is only one even prime number $2$, so set of even prime numbers greater than $2$ is a null set

The collection of good soccer players is not well-defined, because the criterion for determining a soccer as good may vary from person to person, therefore it is not a set.

$A=\{x:x^2-3x+2=0\}$
$x^2-3x+2=0$
$\Rightarrow (x-2)(x-1)=0$
$\Rightarrow x=1,2$
$\Rightarrow A=\{1,2\}$
$B=\{x,x\in N\text{and}|x|\le 2\}$
$|x|\le 2$
$\Rightarrow x\in [-2,2]$
As $x\in N$
$\Rightarrow B=\{1,2\}$
So, $A$ and $B$ are equal sets.

Factors of $8$ are $\{1,2,4,8\}$
Factors of $10$ are $\{1,2,5,10\}$
They are not equal sets.