explain whether each set is closed under the given operation {-1,0,1}multiplication?
Yes, it is closed because if you multiply any of those numbers by any of those other numbers, you will always get one of the numbers in that set.
To determine whether a set is closed under a specific operation, in this case multiplication, we need to check if the result of performing the operation on any two elements within the set still belongs to the set.
Let's examine each element in the given set {-1, 0, 1} and perform multiplication on them:
1. Multiplying -1 by any element in the set:
-1 * -1 = 1 (belongs to the set)
-1 * 0 = 0 (belongs to the set)
-1 * 1 = -1 (belongs to the set)
2. Multiplying 0 by any element in the set:
0 * -1 = 0 (belongs to the set)
0 * 0 = 0 (belongs to the set)
0 * 1 = 0 (belongs to the set)
3. Multiplying 1 by any element in the set:
1 * -1 = -1 (belongs to the set)
1 * 0 = 0 (belongs to the set)
1 * 1 = 1 (belongs to the set)
From the above calculations, we can see that the result of multiplying any two elements from the set {-1, 0, 1} is still an element of the set itself. Therefore, we can conclude that this set is closed under multiplication.