Is this set closed under multiplication
{-1, 0, 1}
Closed under multiplication means that any member of the set times any other member of the set (including itself) yields another member of the set.
We have the combinations,
-1 * 0 = 0
-1 * 1 = -1
-1*-1 = 1
0*0 = 0
0*1 = 0
1*1 = 1
All results are from the set, so it indeed is closed.
To determine if a set is closed under multiplication, we need to check whether the product of any two elements from the set is also in the set.
In this case, the set is {-1, 0, 1}. We can start by multiplying -1 with each element in the set:
-1 * -1 = 1 (not in the set)
-1 * 0 = 0 (in the set)
-1 * 1 = -1 (not in the set)
As we can see, the product of -1 with each element does not result in all elements being in the set. Therefore, we can conclude that the set {-1, 0, 1} is not closed under multiplication.