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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 positive integers a commutative group under the operation of addition?
No. It is not a group.
What is the rule of addition of integers?
negetive integers are not closed under addition but positive integers are.
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 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 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 positive integers a commutative group under the operation of addition?
No. It is not a group.
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.
Example of group is an abelian group?
The set of integers, under addition.
What is the rule of addition of integers?
negetive integers are not closed under addition but positive integers are.
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.
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.
Are integers closed under addition?
yes
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.
Are negative integers closed under multiplication?
No.
