Question

Identify the empty set$,$ the singleton set and the pair set$.$

$C=\{x:x^2=25,x\in N\}$

Answer 1

The given set-builder form is $C=\{x:x^2=25,x\in N\}$

In the set $C$$,$ $x^2=25$ and $x\in N$

$x^2-25=0$

$\left(x-5\right)\left(x+5\right)=0$

$x=5$ or $x=-5$

$5\in N$ but $-5\notin N$

The roster form of the given set-builder form is given below

$C=\left\{5\right\}$

$n\left(C\right)=1$ $,$ the set $C$ is a singleton set.

Hence$,$ the given set $C=\{x:x^2=25,x\in N\}$ is a singleton set.