Yes, that is part of the definition of a group.
A set can be closed or not closed, not an individual element, such as zero. Furthermore, closure depends on the operation under consideration.
Yes.
No. It is not a group.
Division, since you can't divide by zero.
No. The inverses do not belong to the group.
Yes, the Canadian Football League (CFL) is not closed under union operation.
A set can be closed or not closed, not an individual element, such as zero. Furthermore, closure depends on the operation under consideration.
No. It is not even closed. sqrt(3)*sqrt(3) = 3 - which is rational.
Addition.
addition
yes
Yes, they are.
Please clarify what set you are talking about. There are several sets of numbers. Also, "closed under..." should be followed by an operation; "natural" is not an operation.
Subtraction.
Yes.
l think multiplication
Yes, the set of non-deterministic polynomial time (NP) problems is closed under the operation of union.