Respuesta :
One of the operation under which the given set is closed is "Modulus operation".
Given set:
[tex]\{..., -3, -1, 1, 3, ... \}[/tex]
Explanation for closed operations:
Definition: A set is closed under an operation if the operation returns a member of the set when evaluated on members of the set.
Many operations can be defined. But some of the standard operations are known.
From such operations, one operation for which the given set is closed under is modulus operation.
Proof:
[tex]Let \\\\S = \{.., -3, -1, 1,3,...\}\\\\Then \: \forall \: x \in S, \exists -x \in S.\\\\[/tex]
Now let y be any value belonging to S.
Then two cases:
[tex]y < 0:\\ |y| = -y \: which \in S[/tex]
or
[tex]y > 0:\\|y| = y \: which \in S\\\\[/tex]
Thus under modulus operation, the given set is closed.
For more information, refer to:
https://brainly.com/question/7568586
