No, it is not.
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.
1 No. 2 No. 3 Yes.
Yes!
The set of integers is not closed under multiplication and so is not a field.
No, it is not.
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.
1 No. 2 No. 3 Yes.
Yes!
Yes!
The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
Yes
The set of integers is not closed under multiplication and so is not a field.
They are not the same!The set of integers is closed under multiplication but not under division.Multiplication is commutative, division is not.Multiplication is associative, division is not.
Yes.
Yes.
Yes. The empty set is closed under the two operations.