Consider any subset of the real numbers that consists only of negative numbers. What can you conclude about whether the set is closed under multiplication? Explain.

Answer 1

For a set to be closed under multiplication, the product of any two elements in the set must also be an element of the set.

Let S = a set of negative numbers

Let x and y be elements of S

Then, xy > 0. So, xy is not an element of S.

Thus, S is NOT closed under multiplication.