Question

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

$B=\{x:x^2-9=0,x\in Z\}$

Answer 1

The given set-builder form is $B=\{x:x^2-9=0,x\in Z\}$

In the set $B$$,$ $x^2-9=0$ and $x\in Z$

$x^2-9=0$

$\left(x-3\right)\left(x+3\right)=0$

$x=3$ or $x=-3$

$3\in Z$ and $-3\in Z$

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

$B=\left\{-3,3\right\}$

$n\left(B\right)=2$ $,$ the set $B$ is a pair set.

Hence$,$ the given set $B=\{x:x^2-9=0,x\in Z\}$ is a pair set.