Find a counterexample to show the statement is false. the whole number s are closed under division.
Divide any whole number by any other whole number that isn't a factor of it. For example, try dividing 3 by 2. Is the result a whole number?
no because three can not be divided by 2 because its not a factor of three.
To find a counterexample to show that the statement "the whole numbers are closed under division" is false, we need to find two whole numbers such that their division does not result in a whole number.
Whole numbers consist of the natural numbers (1, 2, 3, ...) and zero (0). So, let's consider the whole numbers 4 and 2.
If we divide 4 by 2, we get:
4 ÷ 2 = 2
In this case, the division of two whole numbers does result in a whole number, but we need to find a counterexample, so this does not work.
Let's try dividing a different pair of whole numbers, such as 5 and 2:
5 ÷ 2 = 2.5
Here, when we divide 5 by 2, we get 2.5 which is not a whole number. Therefore, we have found a counterexample that shows the statement "the whole numbers are closed under division" is false.
So, the counterexample is 5 ÷ 2 = 2.5, where 2.5 is not a whole number.