Chapter 4.3, Problem 10E

To determine

To name: The given set of integers.

Answer to Problem 10E

The set of integers is called even integers.

Explanation of Solution

Given:

The following set of integers n:

  $n\equiv 0\left(\mathrm{mod}\text{ 2}\right)$

  $a$ is congruent to $b\left(\mathrm{mod}n\right)$ if $n$ divides the difference $a-b$ .

  $n\equiv 0\left(\mathrm{mod}\text{ 2}\right)$ can be written as $2|\left(n-0\right)=2|n$

Hence, n is divisible by $\text{2}$ . The set of integers that are divisible by $\text{2}$ are called even integers.