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Any set where the result of the multiplication of any two members of the set is also a member of the set.

Well known examples are: the natural numbers (ℕ), the integers (ℤ), the rational numbers (ℚ), the real numbers (ℝ) and the complex numbers (ℂ) - all closed under multiplication.

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Q: Which set is closed under the operation multiplication?

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No. For a set to be closed with respect to an operation, the result of applying the operation to any elements of the set also must be in the set. The set of negative numbers is not closed under multiplication because, for example (-1)*(-2)=2. In that example, we multiplied two numbers that were in the set (negative numbers) and the product was not in the set (it is a positive number). On the other hand, the set of all negative numbers is closed under the operation of addition because the sum of any two negative numbers is a negatoive number.

No. It is not even closed. sqrt(3)*sqrt(3) = 3 - which is rational.

A set is closed under multiplication if for any two elements, x and y, in the set, their product, x*y, is also a member of the set.

yes

Yes.

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Yes.

No. For a set to be closed with respect to an operation, the result of applying the operation to any elements of the set also must be in the set. The set of negative numbers is not closed under multiplication because, for example (-1)*(-2)=2. In that example, we multiplied two numbers that were in the set (negative numbers) and the product was not in the set (it is a positive number). On the other hand, the set of all negative numbers is closed under the operation of addition because the sum of any two negative numbers is a negatoive number.

No. Since -1 x -31 (= 31) would not be in the set.

Is { 0, 20 } closed under multiplication

No. It is not even closed. sqrt(3)*sqrt(3) = 3 - which is rational.

A set is closed under multiplication if for any two elements, x and y, in the set, their product, x*y, is also a member of the set.

Yes!

Yes!

You don't say that "an integer is closed". It is the SET of integers which is closed UNDER A SPECIFIC OPERATION. For example, the SET of integers is closed under the operations of addition and multiplication. That means that an addition of two members of the set (two integers in this case) will again give you a member of the set (an integer in this case).

Yes. The empty set is closed under the two operations.

No.When you multiply two negative numbers together, you do not get a negative number as the answer.

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.