Question

Let $A=\left\{1,3,5,7,.......\right\}$$,$$B=\left\{x:x=2n-1,n\in N\right\}$ and $C=\left\{x:x=4n-1,n\in N\right\}.$ Prove that $A=B$

Answer 1

Given sets $A=\left\{1,3,5,7,.......\right\}$$,$

$B=\left\{x:x=2n-1,n\in N\right\}$ and

$C=\left\{x:x=4n-1,n\in N\right\}.$

Sets $B$ and $C$ can be written in Roster form as below$:$

The elements of the set $B$ are of the form $2n-1$ put $n=1,2,3,4,.....$

$B=\left\{1,3,5,7,.......\right\}$

The elements of the set $C$ are of the form $4n-1$ put $n=1,2,3,4,.....$

$C=\left\{3,7,11,15,.......\right\}$

Set $A=\left\{1,3,5,7,.......\right\}$ and $B=\left\{1,3,5,7,.......\right\}$ have the same elements$.$

Hence$,$ the sets $A$ and $B$ are equal, $A=B$