is the set of all negative numbers closed under the operation of multiplication

Question

understanding of closure and on the multiplication rules for negative numbers

Answer 1

    Closure means that when you take two elements from a set and perform an operation on them, the answer you get is a member of the same set. If this works for all elements from a set, the set is closed under that operation.

 

If  you take any 2 negative numbers and add them, you always get another negative number, so the negative numbers are closed over addition.

 

If you take any 2 negative numbers and multiply them, you always get a positive, NOT A MEMBER of the original set. So negative numbers are not closed over multiplication.

 

If you take the odd integers and addition, their sum is always even.....so not closed.

If you take the odd integers and multiplication, their product is always odd, so this is closed.

Answer 2

The set would be considered closed if every product ab is also a member of the set.

The product ab is a positive number when both a and b are negative so this set is NOT closed under multiplication