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Q: ARe odd integers not closed under addition?

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The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.

Because the set is not closed under addition. If x and y are odd, then x + y is not odd.

The set of even numbers is closed under addition, the set of odd numbers is not.

There is no law of closure. Closure is a property that some sets have with respect to a binary operation. For example, consider the set of even integers and the operation of addition. If you take any two members of the set (that is any two even integers), then their sum is also an even integer. This implies that the set of even integers is closed with respect to addition. But the set of odd integers is not closed with respect to addition since the sum of two odd integers is not odd. Neither set is closed with respect to division.

No. For example, 5 is an odd integer and 3 is an odd integer, yet 5/3 is neither an integer nor odd (as odd numbers are, by definition, integers).

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addition

The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.

Because the set is not closed under addition. If x and y are odd, then x + y is not odd.

The set of even numbers is closed under addition, the set of odd numbers is not.

no

No. 1 + 3 = 4, which is not odd. In fact, no pair of odds sums to an odd. So the set is not closed under addition.

Assuming that the question is in the context of the operation "addition", The set of odd numbers is not closed under addition. That is to say, if x and y are members of the set (x and y are odd) then x+y not odd and so not a member of the set. There is no identity element in the group such that x+i = i+x = x for all x in the group. The identity element under addition of integers is zero which is not a member of the set of odd numbers.

There is no law of closure. Closure is a property that some sets have with respect to a binary operation. For example, consider the set of even integers and the operation of addition. If you take any two members of the set (that is any two even integers), then their sum is also an even integer. This implies that the set of even integers is closed with respect to addition. But the set of odd integers is not closed with respect to addition since the sum of two odd integers is not odd. Neither set is closed with respect to division.

No. For example, 5 is an odd integer and 3 is an odd integer, yet 5/3 is neither an integer nor odd (as odd numbers are, by definition, integers).

1 No. 2 No. 3 Yes.

No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.

Let + (addition) be a binary operation on the set of odd numbers S. The set S is closed under + if for all a, b ϵ S, we also have a + b ϵ S. Let 3, 5 ϵ the set of odd numbers 3 + 5 = 8 (8 is not an odd number) Since 3 + 5 = 8 is not an element of the set of the odd numbers, the set of the odd numbers is not closed under addition.

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