Question

Find the cardinal number of the following sets:
$A_4=\{b:b\in Zand-7<3b-1\le 2\}$

Answer 1

Step : Find the cardinal number of the given set

Given:
$A_4=\{b:b\in Zand-7<3b-1\le 2\}$

As, $-7<3b-1\le 2,(b\in z)$

$\Rightarrow -7<3b-1and3b-1\le 2,b\in Z$

$\Rightarrow -7+1<3band3b\le 2+1,b\in Z$

$\Rightarrow -6<3band3b\le 3,b\in Z$

$\Rightarrow -\frac{6}{3}<bandb\le \frac{3}{3},b\in Z$

$\Rightarrow -2<bandb\le 1,b\in Z$

$\Rightarrow -2<b\le 1,b\in Z$

$\Rightarrow b=-1,0,1$

$\Rightarrow A_4=\{-1,0,1\}$
Number of elements in $A_4$ = 3

We know that the number of distinct element in a finite set is called its cardinal number.

Hence, cardinal number of set $A_4$ is 3.