Checking with Addition:
Let x, y be two whole numbers.
Then, x + y is definitely a whole number.
So, the set of whole numbers is closed under addition.
Checking with Subtraction:
Let x, y be two whole numbers.
Then, x - y may or may not be a whole number.
For example, if we take 3 and 2,
3 - 2 = 1 is a whole number but if we take 2 and 5, then
2 - 5 = -3 is not a whole number.
So, the set of whole numbers is not closed under subtraction.
Checking with Multiplication:
Let x, y be two whole numbers.
Then, x × y is definitely a whole number.
So, the set of whole numbers is closed under multiplication.
Checking with Division:
Let x, y be two whole numbers.
Then, x / y may or may not be a whole number.
For example, if we take 6 and 3,
6/3 = 2 is a whole number.
But, if we take 4 and 5,
4/5 is not a whole number.
So, the set of whole numbers is not closed under division.
