explain whether each set is closed under the given operation {-1,0,1}multiplication?

please help and tell me the steps thanks!

To determine whether a set is closed under a given operation, we need to check if performing that operation on any two elements in the set will always produce another element that is also in the set.

In this case, we have the set {-1, 0, 1} and the operation is multiplication.

To check if the set is closed under multiplication, we perform multiplication on each pair of elements in the set:

1. Multiplying -1 and -1: (-1) x (-1) = 1. The result is not in the set, so the set is not closed under multiplication.

2. Multiplying -1 and 0: (-1) x 0 = 0. The result is in the set.

3. Multiplying -1 and 1: (-1) x 1 = -1. The result is not in the set.

4. Multiplying 0 and 0: 0 x 0 = 0. The result is in the set.

5. Multiplying 0 and 1: 0 x 1 = 0. The result is in the set.

6. Multiplying 1 and 1: 1 x 1 = 1. The result is in the set.

Since there are cases where the result of the multiplication is not in the set, we conclude that the set {-1, 0, 1} is not closed under multiplication.

The steps to determine whether a set is closed under a given operation are as follows:

1. Identify the set and the operation.

2. Perform the operation on each pair of elements in the set.

3. Check if the result of each operation is also in the set.

4. If all the results are in the set, then the set is closed under the operation. If any result is not in the set, then the set is not closed under the operation.

Using this process, you can determine whether a set is closed under any given operation.