The set of integers, rational numbers, real numbers, complex numbers are some of the sets. Also, many of their subsets: for example, all numbers divisible by 3.
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Not by itself. A mathematical operation has properties in the context of a set over which it is defined. It is possible to have a set over which properties are not valid.Having said that, the set of rational numbers is closed under subtraction, as is the set of real numbers or complex numbers.Multiplication is distributive over subtraction.
It means whatever members of the set you subtract, the answer will still be a member of the set. For example, the set of positive integers is not closed under subtraction, since 3 - 8 = -5
Yes.
1 No. 2 No. 3 Yes.
A set can be closed or not closed, not an individual element, such as zero. Furthermore, closure depends on the operation under consideration.