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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.
Are integers closed under addition?
yes
Are negative integers closed under multiplication?
No.
Is the set of all negative integers a group under addition?
no
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.
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 integers closed under addition?
yes
Are negative integers closed under multiplication?
No.
Is the set of integers closed under addition?
Yes it is.
