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Is the set of all negative numbers closed under the operation of multiplication Explain why or why not?

Wiki User

2009-11-21 03:16:05

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.

Wiki User

2009-11-21 03:16:05
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Q: Is the set of all negative numbers closed under the operation of multiplication Explain why or why not?
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