Question

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 $X\to Y$?

• A. $R_1=\left\{\right(x,y)\mid y=2+x,x\in X,y\in Y\}$
• B. $R_2=\left\{\right(1,1),(2,1),(3,3),(4,3),(5,5\left)\right\}$
• C. $R_3=\left\{\right(1,1),(1,3),(3,5),(4,7),(5,7\left)\right\}$
• D. $R_4=\left\{\right(1,3),(2,5),(3,4),(4,9\left)\right\}$

Answer 1

Answer: (A), (C), (D)

$R_4=\left\{\right(1,3),(2,5),(3,4),(4,9\left)\right\}$

$R_1$ 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