Chapter C, Problem 1E

Decide whether each relation defines a function. See Example 1.

{(5, 1), (3, 2), (4, 9), (7, 8)}

To determine

Whether the given relation $\left\{\left(5,1\right)\left(3,2\right)\left(4,9\right),\left(7,8\right)\right\}$ defines a function or not.

Answer to Problem 1E

Solution: The given relation is a function.

Explanation of Solution

Given: The relation $\left\{\left(5,1\right)\left(3,2\right)\left(4,9\right),\left(7,8\right)\right\}$.

A function is defined as a relation in which for each distinct value of the first component, there is exactly one value of the second component.

Consider the relation $\left\{\left(5,1\right)\left(3,2\right)\left(4,9\right),\left(7,8\right)\right\}$.

The set of distinct values of the first component is $\left\{5,3,4,7\right\}$.

Each element of this set is paired with exactly one value of the second component.

This correspondence is as follows:

$\begin{array}{c}5\to 1\\ 3\to 2\\ 4\to 9\\ 7\to 8\end{array}$

Therefore, the relation is a function.

Hence, the relation is a function.