Yes. The entire set of natural numbers is closed under addition (but not subtraction). So are the even numbers (but not the odd numbers), the multiples of 3, of 4, etc.
It is not closed under taking square (or other even) roots.
Yesss.
Yes, because suppose that 'a' and 'b' are both arbitrary integers. Then (a-b) or (b-a) will then provide you with another integer. Suppose that the integer you are given from (a-b) is not unique. Then we have: (a-b)=c and (a-b)=c' Then, trivially, since (a-b)=(a-b), we have c=c'. Thus it is closed under subtraction.
For a set to be closed under an operation, doing the operations on any two members of the set must result in another member of the set.The set of even natural numbers is {2, 4, 6, ...}.When two even numbers are added, the result is also an even number.Adding two positive numbers results in a larger positive number.Thus, adding two even natural numbers together results in another even natural number and so is closed.The set of even whole numbers is {..., -6, -4, -2, 0, 2, 4, 6, ...}.When two even numbers are added, the result is also an even number.It does not matter which combination of positive and negative whole numbers are added as all positive and negative whole numbers (including zero) are in the set. Thus it is also closed under addition.
Yes. The entire set of natural numbers is closed under addition (but not subtraction). So are the even numbers (but not the odd numbers), the multiples of 3, of 4, etc.
The set of even numbers is closed under addition, the set of odd numbers is not.
Subtraction: Yes. Division: No. 2/4 = is not an integer, let alone an even integer.
The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
It is not closed under taking square (or other even) roots.
Yesss.
Yes, it is closed. This means that if you multiply two even number, you again get a number within the set of even numbers.
Yes, when you add any two even numbers, the result is always an even number.
Yes, because suppose that 'a' and 'b' are both arbitrary integers. Then (a-b) or (b-a) will then provide you with another integer. Suppose that the integer you are given from (a-b) is not unique. Then we have: (a-b)=c and (a-b)=c' Then, trivially, since (a-b)=(a-b), we have c=c'. Thus it is closed under subtraction.
No. 2/4 is not an even number.
Unfortunately, the term "whole numbers" is somewhat ambiguous - it means different things to different people. If you mean "integers", yes, it is closed. If you mean "positive integers" or "non-negative integers", no, it isn't.
Yes, the sum of any two even numbers is an even number. This means they are closed under addition. Closure Property: For every even number a, for every even number b, a + b is an even number.