Are the following set of ordered pairs functions?

(i) Given, {(x, y): x is a person, y is the mother of x}

It’s clearly seen that each person ‘x’ has only one biological mother.

Hence, the above set of ordered pairs make a function.

Now more than one person may have same mother. Thus, the function is many-many one and surjective.

(ii) Given, {(a, b): a is a person, b is an ancestor of a}

It’s clearly seen that any person ‘a’ has more than one ancestors.

Thus, it does not represent a function.