Question

Write the cardinal number for the set $B=\left\{x:x=2n,n\in W,n\le 5\right\}$

Answer 1

Cardinal number is the number of elements in a set.

In the given set, $n\in W$, i.e., whole numbers ( numbers which begin from $0$ to infinity) and $n\le 5$.

$\therefore n=0,1,2,3,4,5$,

Therefore, putting values of $n$ in $x=2n$

For $n=0,x=2\times 0=0$

For $n=1,x=2\times 1=2$

For $n=2,x=2\times 2=4$

For $n=3,x=2\times 3=6$

For $n=4,x=2\times 4=8$

For $n=5,x=2\times 5=10$

We get set $B=\left\{0,2,4,6,8,10\right\}$.

The number of elements will be $6$.

Hence cardinal number for the set $B$ will be $n\left(B\right)=6$.