Chapter 4.6, Problem 31PPE

To determine

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

Answer to Problem 31PPE

The given relation $\left\{\left(a,b\right),\left(b,a\right),\left(c,c\right),\left(e,d\right)\right\}$ is a function.

Explanation of Solution

Given information :

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

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 in each pair every $x$ element is associated with a singles $y$ element.

Therefore, given relation $\left\{\left(a,b\right),\left(b,a\right),\left(c,c\right),\left(e,d\right)\right\}$ is a function.