Suppose Z denotes the set of all integers, Zopf^+ denotes the set of all positiv

Question

Suppose Z denotes the set of all integers, Zopf^+ denotes the set of all positive integers, and Zopf^- denotes the set of all negative integers. Similarly R denotes the set of all real numbers, Ropf+ denotes the set of all positive real numbers, and Ropf- denotes the set of all negative real numbers. Suppose Nopf denotes the set of all natural numbers and Qopf denotes the set of all rational numbers. Enter "T" for each true, and "F" for each false statements. F Z Qopf = Z F empty SubsetEqual Zopf^+ T Z Qopf = empty F Z Zopf^- = Zopf^+ T Nopf = Zopf^+ cup {0} T Z Zopf^- = Nopf T {0} cup Zopf^+ = Nopf T Z^+ SubsetEqual Nopf T Qopf cup R = R F Ropf^+ Zopf^+ = Qopf^+ F Nopf SubsetEqual Zopf^+ F Zopf^+ cup Zopf^- = Zopf

Explanation / Answer

1. False

2. False because Z+ doesn't contain null set

3. True

4. False because solution contains null set but Z+ doesn't contain null set

5. False because natural set doesn't contain null set

6. False

7. False

8. True

9. True

10. False

11. True

12. False

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