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Let $A = {p, q, r, s}$ and $B = {1, 2, 3}$ . Which of the following relations from $A$ to $B$ is not a function?

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$R_{1} = {(p, 1), (q, 2), (r, 1), (s, 2)}$

$R_{2} = {(p, 1), (q, 2), (r, 1), (s, 1)}$

$R_{3} = {(p, 1), (q, 2), (r, 2), (r, 2)}$

$R_{4} = {(p, 2), (q, 3), (r, 2), (s, 2)}$

answer is C.

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Detailed Solution

Given,

$A = {p, q, r, s}$ and,

$B = {1, 2, 3}$

In case of $R_{3} = {(p, 1), (q, 2), (r, 2), (r, 2)}$ , $x$ - coordinates of two brackets are same.

Hence, relations from $A$ to $B$ is not a function.

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