Question

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

• A. $R_1=\left\{\right(p,1),(p,2),(r,1),(s,2\left)\right\}$
• B. $R_2=\left\{\right(p,1),(q,2),(r,1),(s,1\left)\right\}$
• C. $R_3=\left\{\right(p,1),(q,2),(r,2),(r,2\left)\right\}$
• D. $R_4=\left\{\right(p,2),(q,3),(r,2),(s,2\left)\right\}$

Answer 1

Answer: (A), (C)

$R_1=\left\{\right(p,1),(p,2),(r,1),(s,2\left)\right\}$
$R_3=\left\{\right(p,1),(q,2),(r,2),(r,2\left)\right\}$

The relation which has only one value of $y$ for every $x$ which appears in option $B,D$

but in option $A,C$ we found every $x$ has two values of $y$. hence these are relation are not functions.