Question

State which of the following are finite sets.
$\left(i\right)\{x:x\in N\}$ and $(x-1)(x-2)=0.$
$\left(ii\right)\{x:x\in N\}$ and $x$ is prime.
$\left(ii\right)\{x:x\in N\}$ and $x$ is odd.

• A. $\left(i\right)$ only
• B. $\left(i\right),\left(ii\right)$ and $\left(iii\right)$
• C. $\left(i\right)$ and $\left(ii\right)$
• D. $\left(ii\right)$ and $\left(iii\right)$

Answer 1

Answer: (A)

$\left(i\right)$ only

$\left(i\right)(x-1)(x-2)=0$

$\Rightarrow x-1=0$ or $x-2=0$

$\Rightarrow x=1$ or $x=2$, Number of solutions of equation are finite.

$\left(ii\right)\{2,3,5,7,11,...\}$, This set contains infinte number of elements.

$\left(iii\right)\{..,1,3,5,7,...\}$, This set contains infinite number of elements.