Question

Are the following sets of ordered pairs functions? If so, examine wheather the mapping is surjective or injective.
(a) {(x,y):x is a person, y is the mother of x}

Answer 1

Given $\left\{\right(x,y):x$ is a person, $y$ is the mother of $x\}$
Every person has a mother and that too unique and hence it is a mapping.

Since two or more persons can have the same mother and hence it is many-one.

Again every mother has a child (person). Hence it is onto. i.e. surjective.

So, the given set of ordered pairs is surjective but not injective.