Question

Tell whether the set is closed under the operation. If it is not closed give an example that shows that the set is not closed under the operation.

10. Positive irrational numbers; division
11. Negative rational numbers; multiplication
12. Negative integers; addition
13. Positive integers; subtraction

Answer 1

yes: 12
no: 10,11,13
√2/√2 = 1
-2/3 * -3/2 = 1
3-2 = -1

Answer 2

just tell me if ,Under the set of rational numbers is -9 + 12 closed?

Answer 3

Give one counter example for each that the set of irrational number is not closed under the operations of addition, substraction, multiplication and division