Question

Which of the following sets is a finite set?

• A. $A=\left\{x:x\in Zand{x}^2-5x+6=0\right\}$
• B. $B=\left\{x:x\in Zand{x}^{2}iseven\right\}$
• C. $D=\left\{x:x\in Zandx>-10\right\}$
• D. All of these

Answer 1

The correct option is A

$A=\left\{x:x\in Zand{x}^2-5x+6=0\right\}$

Explanation for the correct option:

Option A: $A=\left\{x:x\in Zand{x}^2-5x+6=0\right\}$

Factorizing the equation by splitting the midterm

$x^2-5x+6=0$

$\Rightarrow$ ,$x^2-3x-2x+6=0$

$\Rightarrow$$x\left(x-3\right)-2\left(x-3\right)=0$

$\Rightarrow$ $\left(x-2\right)\left(x-3\right)=0$

$\Rightarrow$ $x=2,3$

The set $A=\left\{2,3\right\}$ is a finite set.

Explanation for the incorrect options:

Option B: $B=\left\{x:x\in Zand{x}^{2}iseven\right\}$

The set $B=\left\{....,-8,-6,-4,-2,2,4,6,8........\right\}$ is an infinite set.

Option C: $D=\left\{x:x\in Zandx>-10\right\}$

The set $D=\left\{-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,......\right\}$ is an infinite set.

Hence the correct option is A.