Chapter 4.6, Problem 36PPE

To determine

To write : an example of a relation that is a function but whose inverse is not a function.

Answer to Problem 36PPE

  $R=\left\{\left(1,8\right)\left(2,8\right),\left(3,9\right)\right\}$

Explanation of Solution

Solution:

Consider a relation

  $R=\left\{\left(1,8\right)\left(2,8\right),\left(3,9\right)\right\}$

The domain of the relation is X={ 1,2,3} and range of the relation is Y={ 8,9}.

This relation is a function from X to Y since each element from X is related to only one element in Y.

Now, inverse of relation R is

  $R^{-1}=\left\{\left(8,1\right)\left(8,2\right),\left(9,3\right)\right\}$

This relation is not a function from Y to X as the element 8 in Y is related to two elements 1 and 2 in X.