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โˆ™ 2012-08-08 17:21:08
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Q: Under which operation is the set of odd integers closed?
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Related questions

Which set is closed under the given operation 1 integers under division 2 negative integers under subtraction 3 odd integers under multiplication?

1 No. 2 No. 3 Yes.


ARe odd integers not closed under addition?

That is correct, the set is not closed.


Why are odd integers closed under multiplication but not under addition?

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


Why the set of odd integers under addition is not a group?

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


Is the set of odd integers closed under 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).


What are examples of the law of closure in Mathematics?

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.


Give two reason for the set of odd integers is not a group?

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.


Is the set of odd integers closed under subtraction?

No.To say a set is closed under subtraction means that if you subtract any 2 numbers in the set, the answer will always be a member of the set. If you subtract 3 from11, the answer is 8, which is not an odd number. Actually, when you subtract odd numbers, you always get an even number!


Is the set of odd numbers is closed under multiplication but is not under addition?

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.


What the probability of an odd number?

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.


What is closed and not-closed under addition?

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


Are odd numbered sets closed under addition and multiplication?

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.

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