under which operation is the set
{-1,0,1} closed?
1 multiplication
2 addititon
3 division
4 subtraction
To determine under which operation a set is closed, we need to perform the given operation with any two elements from the set and check if the result also belongs to the set.
For the set {-1, 0, 1}, let's evaluate the given operations:
1) Multiplication:
-1 * 0 = 0 (0 is in the set)
-1 * 1 = -1 (-1 is in the set)
0 * 1 = 0 (0 is in the set)
From these results, we see that multiplication is not a closed operation for this set.
2) Addition:
-1 + 0 = -1 (-1 is in the set)
-1 + 1 = 0 (0 is in the set)
0 + 1 = 1 (1 is in the set)
Based on these results, addition is a closed operation for this set.
3) Division:
Since division involves dividing by zero, it is undefined in this case. Therefore, we cannot consider division as a possible operation for this set.
4) Subtraction:
-1 - 0 = -1 (-1 is in the set)
-1 - 1 = -2 (-2 is not in the set)
0 - 1 = -1 (-1 is in the set)
From these calculations, subtraction is not a closed operation for this set.
Therefore, the set {-1, 0, 1} is closed under addition (option 2).