Question

$f,h$ are relations from $A$ to $B$ where $A=\{a,b,c,d\}$, $B=\{s,t,u\}$ defined as $f\left(a\right)=t,f\left(b\right)=s,f\left(c\right)=s,f\left(d\right)=u,h\left(a\right)=s,h\left(b\right)=t,h\left(c\right)=s,h\left(a\right)=u,h\left(d\right)=u$ which of the following is true

• A. $f,h$ are functions
• B. $f$ is a function, but $h$ is not a function
• C. $h$ is a function, but $f$ is not a function
• D. neither $f$ nor $h$ is a function

Answer 1

The correct option is B $f$ is a function, but $h$ is not a function

A function is a relation, for which each value from the set of first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair. i.e.

$f,h$ are defined as $f\left(a\right)=t,f\left(b\right)=s,f\left(c\right)=s,f\left(d\right)=u,h\left(a\right)=s,h\left(b\right)=t,h\left(c\right)=s,h\left(a\right)=u,h\left(d\right)=u$

In $f:A\to B$,

$f$ is many one relation ,hence function

But in $h:A\to B$, $a$ is associated with two elements i.e. $s,u$ of $B$.

Thus, $h$ is not a function.

Hence, option B is correct.