Question

$f$ and $h$ are relations from $A\to B$ where $A=\left\{a,b,c,d\right\}$; $B=\left\{s,t,u\right\}$ defined as follows:
$f\left(a\right)=t,f\left(b\right)=s,f\left(c\right)=s,f\left(d\right)=u$;
$h\left(a\right)=s,h\left(b\right)=t,h\left(c\right)=s,h\left(a\right)=u,h\left(d\right)=u$
Which one of the following statement is true?

• A. $f$ and $h$ are function
• B. $f$ is a function and $h$ is not a function
• C. $f$ and $h$ are not functions
• D. none of these

Answer 1

The correct option is B $f$ is a function and $h$ is not a function

Consider the relation $f:A\to B$. For every element of set $A$ there exist a unique element from set $B$. Hence the relation $f:A\to B$ is a function.from set $A$ to set $B$.
Note that for relation $h:A\to B$, an element $a$ is mapped to two different elements from set $B$, namely, $s$ and $u$. Hence the relation $h$ is not a function.