Let A x x is a nation B Asia Africa North America South Am

Let A = {x| x is a nation}

          B = {Asia, Africa, North America, South America, Antarctica, Europe, Australia}

Let f:A?B be the function that outputs the continent to which a nation belongs. For example, f(Iceland) = Europe and f(Greenland) = North America. Explain why f is not a one-to-one function and give an example to prove it

Solution

In order for the function to be a one-one, for every element of A there must exists a unique element in B, i.e. no two values in function A can be mapped to a single value in B

This function is not one-one since there are many nations which belong to the same continent, hence the mapping of each and every nation belonging to the same continent will be same => this function is not one-one

Example:

India is part of Asia and Chinal is also a part of Asia

f(India) = Asia

f(China) = Asia

Hence both the function value for India and China will mapped to Asia => the function is not one-one