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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.
What is closed and not-closed under addition?
The set of even numbers is closed under addition, the set of odd numbers is not.
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.
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).
