Question

Which operations is the following set closed under: {... , -3, -1, 1, 3, ...}?

Answer 1

The set {... , -3, -1, 1, 3, ...} is closed under the operation of multiplication.

• The given set is a set of odd numbers.
• We know that any odd number when multiplied by another odd number gives an odd number.

• But, the same is not true in the case of addition, subtraction and division.
• Thus, we can conclude that the give set of odd numbers is closed under the operation of multiplication.