No. The additive identity, 0, is the only value such that A*0 = 0 for any non-zero element A of the set.
Is the set of negative interferes a group under addition? Explain,
Yes it is.
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.
Yes.
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 interferes a group under addition? Explain,
Yes it is.
addition
no
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.
Yes.
That is correct, the set is not closed.
Because the set is not closed under addition. If x and y are odd, then x + y is not odd.
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.
No. It is not a group.
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).
Yes, all integers are closed under addition. This means that when you add any two integers together, the result is always another integer. For example, adding -3 and 5 yields 2, which is also an integer. Therefore, the set of integers is closed under the operation of addition.