Q: Under which operation is the set of odd integers closed?

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no

you can say that 2/10 of every 10 integers is divisible by 5, so multiplying 2/10 by 100, giving you 200/1000 total integers are divisible by 5. half of all integers are odd, so divide 200/1000 by 2 is 100/1000, so you can correctly state that 100 odd integers under 1000 are divisible by 5.

The sum of the first 2,006 positive, odd integers is 4,024,036.

The first odd positive integers are "1" and "3" which the sum is 4.

No. Even and odd are properties of integers only.

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1 No. 2 No. 3 Yes.

That is correct, the set is not closed.

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.

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).

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.

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.

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.

The answer depends on what set of integers is under consideration.The answer depends on what set of integers is under consideration.The answer depends on what set of integers is under consideration.The answer depends on what set of integers is under consideration.

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

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.

no