If $X = {1, 2, 3, 4, 5}$ and $Y = {1, 3, 5, 7, 9}$ , then which of the following relation(s) is/are not a function from $X \to Y$ ?

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Solution

$R_{1}$ is not a function from $X$ to $Y,$ because there are no images of $2, 4$ present in $Y$

$R_{3}$ is not a function from $X$ to $Y,$ because there are two images of $1$ present in $Y$

$R_{4}$ is not a function from $X$ to $Y,$ because $4$ is not present in $Y$ and the image is $5$ is not defined

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