A set can be closed or not closed, not an individual element, such as zero.
Furthermore, closure depends on the operation under consideration.
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Yes because being closed under an operation means that when the operation is performed on members of a set the result is also a member of the set, and when any two [members of the set of] whole numbers are added together the result of the addition is also a whole number which is, unsurprisingly, a member of the set of whole numbers.
The whole numbers are not closed under division! The statement is false since, for example, 2/3 is not a whole number.
No. Since -1 x -31 (= 31) would not be in the set.
Yes.
Yes. When you add any whole numbers you get another whole number. That is what closed means in this context. The answer is still a whole number.