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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.
Is the set of negative integers is closed under addition?
No, the set of negative integers is not closed under addition. When you add two negative integers, the result is always a negative integer. However, if you add a negative integer and a positive integer, the result can be a positive integer, which is not in the set of negative integers. Thus, the set does not satisfy the closure property for addition.
Is the set of even integers closed under addition and multiplication?
Yes.
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 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 negative integers is closed under addition?
No, the set of negative integers is not closed under addition. When you add two negative integers, the result is always a negative integer. However, if you add a negative integer and a positive integer, the result can be a positive integer, which is not in the set of negative integers. Thus, the set does not satisfy the closure property for addition.
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.
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.
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.
Why are the set of integers closed under addition?
The set of integers is closed under addition because the sum of any two integers is always an integer. This means that when you add two whole numbers, whether they are positive, negative, or zero, the result will still belong to the set of integers. For example, adding -3 and 5 results in 2, which is also an integer. Hence, this property ensures that no matter which integers are selected for addition, the outcome remains within the set of integers.
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).
