First a definition:
A given set is closed under a given operation if, for any given pair of elements of the set under that operation, the outcome also belongs to the set.
With this, we will find that the set of integer numbers is not closed under division.
Now let's be more clear.
The definition particularly means that a set is closed under division only if for any pair of elements of the set, the division of these elements also does belong to the set.
Here we want to see if the set of integers is closed under division. To see that this is false, we just need to find a counterexample.
This is, finding a pair of integer numbers that have a quotient that is not an integer.
A really simple example is:
1 and 2.
2/1 = 2 is integer.
but
1/2 = 0.5 is not integer.
Thus we can conclude that the set of integers is not closed under division.
If you want to learn more, you can read:
https://brainly.com/question/17175273
