Question

Are the following set of ordered pairs functions? If so examine whether the mapping is injective or surjective.

(i) $f=\left\{\right(x,y):\text{x is a person, y is the mother of x}\}$

(ii) $g=\left\{\right(a,b):\text{a is a person, b is the ancestor of a}\}$

Answer 1

(i) Given set of ordered pair is $\left\{\right(x,y):\text{x is a person, y is the mother of x}\}$. It represents a function since every person can have one and only one mother. Here, the image of distinct elements of x under f need not be distinct i.e. two people can have the same mother. So it is not a injective but it is a surjective.

(ii) Set of ordered pairs $g=\left\{\right(a,b):\text{a is a person, b is the ancestor of a}\}$. Here, each element of the domain does not have a unique image. So, $g$ does not represent a function.