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Question 20565: Is the following true or false?
The set of whole numbers is closed under subtraction
The set of whole numbers is closed under multiplication
The set of whole numbers is closed under division
Thanks,
Teri
Answer by askmemath(368)   (Show Source):
You can put this solution on YOUR website! First of all,let us start be defining the term "closed"
A set of numbers is said to be closed for an operation, if upon performing that operation between the numbers you get a member of that set.
For e.g
Consider the set of whole numbers. Whole numbers are (1,2,3,4,5......)
Now,take any 2 numbers and add them. Say 5 and 6. The sum we get is 11 which as we know is a whole number.
Now we can say that the set of Whole Numbers is closed under Addition.
Consider Subtraction.
6-5 = 1
But 5-6 = -1 which is not a whole number.
So the set of Whole Numbers is NOT closed under Subtraction.
Can you try for Multiplication and Division?
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