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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 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 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.
Examples to prove the set of integers is a group with respect to addition?
In order to be a group with respect to addition, the integers must satisfy the following axioms: 1) Closure under addition 2) Associativity of addition 3) Contains the additive identity 4) Contains the additive inverses 1) The integers are closed under addition since the sum of any two integers is an integer. 2) The integers are associative with respect to addition since (a+b)+c = a+(b+c) for any integers a, b, and c. 3) The integer 0 is the additive identity since z+0 = 0+z = z for any integer z. 4) Each integer n has an additive inverse, namely -n since n+(-n) = -n+n = 0.
ARe odd integers not closed under addition?
That is correct, the set is not closed.
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 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.
