No.
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 integers are closed under multiplication. This means that when you multiply any two integers together, the result is always an integer. For example, multiplying -3 and 4 yields -12, which is also an integer. Therefore, the set of integers is closed under the operation of multiplication.
The set of negative rational integers is closed under the operations of addition and multiplication. This means that when you add or multiply any two negative rational integers, the result will also be a negative rational integer. However, it is not closed under subtraction, as subtracting a larger negative integer from a smaller one can result in a non-negative integer.
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 integers are closed under multiplication. This means that when you multiply any two integers together, the result is always an integer. For example, multiplying -3 and 4 yields -12, which is also an integer. Therefore, the set of integers is closed under the operation of multiplication.
To determine if a set is closed under multiplication, we need to check if the product of any two elements from the set is also an element of the same set. For example, the set of integers is closed under multiplication because the product of any two integers is always an integer. In contrast, the set of natural numbers is also closed under multiplication, while the set of rational numbers is closed under multiplication as well. However, sets like the set of positive integers and the set of even integers are also closed under multiplication.
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.
Yes.
Yes.