Chapter 4.6, Problem 32PPE

To determine

Whether the relation $\left\{\left(b,b\right),\left(c,d\right),\left(d,c\right),\left(c,a\right)\right\}$ is a function or not.

Answer to Problem 32PPE

The given relation $\left\{\left(b,b\right),\left(c,d\right),\left(d,c\right),\left(c,a\right)\right\}$ is not a function.

Explanation of Solution

Given information :

Given relation $\left\{\left(b,b\right),\left(c,d\right),\left(d,c\right),\left(c,a\right)\right\}$

As we know that a relation is said to be a function if every element of $x$ is associated with a single $y-$ element.

Thus, from given relation we observe that the $x$ element $c$ is associated with two element’s of $y$ .

i.e. $c\to d,a$

Therefore, the given relation $\left\{\left(b,b\right),\left(c,d\right),\left(d,c\right),\left(c,a\right)\right\}$ is not a function.