The figure given below shows a relation from $P$ to $Q .$ Find the relation, domain and range from the arrow diagram given?

R = {(x, y): y is the square of x , $x \in P, y \in Q$ }, Domain = {9, 4, 25, 36}, Range = {-2, 2, -3, 3, -4, 4, -5, 5}

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R = {(x, y): x is the square of y, $x \in P, y \in Q$ }, Domain = {9, 4, 25, 36}, Range = {-2, 2, -3, 3, -5, 5, -6, 6}

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R = {(x, y): y is the square of x, $x \in P, y \in Q$ }, Domain = {9, 4, 25, 36}, Range = {-2, 2, -3, 3, -5, 5, -6, 6, -4, 4}

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R = {(x, y): x is the square of y where $x \in P, y \in Q$ }, Domain = {9, 4, 25}, Range = {1, -2, 2, -3, 3, -4, 4}

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Solution

The correct option is B
R = {(x, y): x is the square of y, $x \in P, y \in Q$ }, Domain = {9, 4, 25, 36}, Range = {-2, 2, -3, 3, -5, 5, -6, 6}

From the arrow diagram, it is clear that $R = {(9, 3), (9, - 3), (4, 2), (4, - 2), (25, 5), (25, - 5), (36, 6), () 36, - 6} .$
$\Rightarrow x R y$ means $x$ is the square of $y,$ where $x \in P$ and $y \in Q .$
Also, domain of $R = {9, 4, 25, 36} .$
$Range of R = {- 2, 2, - 3, 3, - 5, 5, - 6, 6}$

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