Are the following set of ordered pairs functions?
If so examine whether the mapping is injective or surjective.
(i) $\{ (x,y):x$ is a person, $y$ is the mother of $x\}$.
(ii) $\{ (a,b):a$ is a person, $b$ is an ancestor of $a\}$.

(i) Given set of ordered pair is $\{ (x,y):x$ is

a person, $y$ is the mother of $x\}$.

It represent a function. Here, the image of

distinct elements of $x$ under $f$ are not

distinct, so it is not a injective but it is a

surjective.

(ii) Set of ordered pairs $= \{ (a,b):a$ is a person, $b$ is an ancestor of $a\}$

Here, each element of domain does not have a

unique image. So, it does not represent function.