Let's start by discussing what a Closure Property is. To define a Closure Property, we need to specify a set of numbers and an operation. Then, if we can apply the operation in question to any pair of numbers from the set, such that the result is also a number of the set, we say that the set is closed under the operation. Now, let's go back to our case.
Set of numbers
Operation
Whole numbers
{ 0, 1, 2, 3, 4, ... }
Subtraction
``-"
In this case we are considering the set of whole numbers, which are all integers equal or greater than 0, and our operation is subtraction. We can prove that a Closure Property for whole numbers under subtraction is not possible if we can find a counterexample.
Note that 2 and 3 belong to the set of whole numbers.
{ 0, 1, 2, 3, 4, ... }
Now, let's apply the operation we are testing — in this case, subtraction.
2-3= -1
Since -1 is not an element of the set of whole numbers, by definition of a Closure Property the set of whole numbers is not closed under subtraction.
