Question

Let $A=\{1,4,9,25\}$ and $B=\{-5,-3,-2,-1,1,2,3,5\}$, if relation from $A$ to $B$ is $R=\left\{\right(1,1),(1,-1),(4,2),(4,-2),(9,3),(9,-3),(25,5),(25,-5\left)\right\}$, then the set builder form of relation is

• A. $R=\left\{\right(x,y);y=x^2,x\in A,y\in B\}$
• B. $R=\left\{\right(x,y);y=|x|,x\in A,y\in B\}$
• C. $R=\left\{\right(x,y);y^2=x,x\in A,y\in B\}$
• D. $R=\left\{\right(x,y);y=\sqrt{x},x\in A,y\in B\}$

Answer 1

The correct option is C $R=\left\{\right(x,y);y^2=x,x\in A,y\in B\}$

Let $a,b$ be the elements such that $a\in A$ and $b\in B$
Here, $1=1^2$
$1=(-1{)}^2$
$4=(2{)}^2=(-2{)}^2$
$9=(3{)}^2=(-3{)}^2$
​​​​​​​$25=(5{)}^2=(-5{)}^2$
We can see that for every $a\in A$ and $b\in B$ in relation $R$, we get
$a=b^2$
So, the set builder form of relation $R$ will be $R=\left\{\right(x,y);y^2=x,x\in A,y\in B\}$