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Is the set of negative integers a group under addition?
Is the set of negative interferes a group under addition? Explain,
Is the set of integers closed under addition?
Yes it is.
Under which operation is the set of odd integers closed?
addition
Is the set of all negative integers a group under addition?
no
Is the set of even integers closed under addition and multiplication?
Yes.
ARe odd integers not closed under addition?
That is correct, the set is not 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 the set of whole numbers closed by?
If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.
Is the set of positive integers a commutative group under the operation of addition?
No. It is not a group.
What does it mean if an integer is closed?
You don't say that "an integer is closed". It is the SET of integers which is closed UNDER A SPECIFIC OPERATION. For example, the SET of integers is closed under the operations of addition and multiplication. That means that an addition of two members of the set (two integers in this case) will again give you a member of the set (an integer in this case).
Why is a set of positive integers not a group under the operation of addition?
The set of positive integers does not contain the additive inverses of all but the identity. It is, therefore, not a group.
Why is zero important in a set of integers?
It provides closure under the binary operation of addition.
