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I going to denote the operations in this manner:
Addition → A
Subtraction → S
Multiplication → M
Division → D
And let O denote any of the above operations.
(For example, aOb may represent a+b or a-b or a×b or a÷b (only when b≠0)).
For any set T, operation O is said to be closed in set T if for all a, b ∈T ⇒ aOb∈T.
Answers to the questions:
1. A, M, D
2. A, M, D
3. M
4. A, M, D
5. None
6. None
7. M, D
8. None
9. None
10. A, M
11. A, M
12. A, S, M
13. A, S, M
14. A, S, M, D
15.A, S, M, D
Additional question:
Rational number set (Q) : A, S, M, D
Irrational number set (Q') : A, S
1 5 1