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Earn +20 ptsQ: Does a group have to be closed under its operation?
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Why is zero not closed under the operation of whole numbers?
A set can be closed or not closed, not an individual element, such as zero. Furthermore, closure depends on the operation under consideration.
Is the set of all integers closed under the operation of multiplication?
Yes.
Is the set of positive integers a commutative group under the operation of addition?
No. It is not a group.
The set of real numbers are NOT closed under which operation?
Division, since you can't divide by zero.
Does the set of even integers form a group under the operation of multiplication?
No. The inverses do not belong to the group.
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