Question

Two sets $X$ and $Y$ are given such that
$X=\{54,79,38\}\&Y=\{32,44,86\}$. Which of the below relations from set $X$ to set $Y$ are functions?

• A. $f_1=\left\{\right(54,32),(79,44),(38,86\left)\right\}$
• B. $f_2=\left\{\right(54,32),(54,44),(79,44),(38,86\left)\right\}$
• C. $f_3=\left\{\right(54,86),(38,32\left)\right\}$
• D. All are functions

Answer 1

The correct option is A $f_1=\left\{\right(54,32),(79,44),(38,86\left)\right\}$

$\underset{–}{Option\left(a\right)}$
Every element of set $X$ is uniquely related to the element of set $Y$ so $f_1$ is Function.

$\underset{–}{Option\left(b\right)}$ $54$ is related to $32$ as well as $44$, so it is NOT function.

$\underset{–}{Option\left(c\right)}$ Each element of set $X$ is not related with elements of Set $Y$. Hence it is also NOT a function.