Problem Set 2
Question 2.1. Problem 1 on page 14 of Chiang (2005).
Question 2.2. Problem 2 on page 14 of Chiang (2005).
Question 2.3. Problem 3 on page 14 of Chiang (2005).
Question 2.4. Problem 4 on page 14 of Chiang (2005).
Question 2.5. Problem 5 on page 14 of Chiang (2005).
Question 2.6. Problem 7 on page 14 of Chiang (2005).
Question 2.7. Problem 8 on page 14 of Chiang (2005).
Question 2.8. Problem 1 on page 19 of Chiang (2005).
Question 2.9. Problem 2 on page 19 of Chiang (2005).
Question 2.10. Problem 3 on page 19 of Chiang (2005).
Question 2.11. Problem 4 on page 19 of Chiang (2005).
Question 2.12. Problem 5 on page 19 of Chiang (2005).
Question 2.13. Problem 6 on page 20 of Chiang (2005).
Question 2.14. Problem 1 on page 24 of Chiang (2005).
Question 2.15. Problem 2 on page 24 of Chiang (2005).
Question 2.16. Problem 3 on page 25 of Chiang (2005).
Question 2.17. Problem 4 on page 25 of Chiang (2005).
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Question 2.18. Prove (𝑆𝑆 ∩ 𝑇𝑇)𝑐𝑐 = 𝑆𝑆 𝑐𝑐 ∪ 𝑇𝑇 𝑐𝑐 and (𝑆𝑆 ∪ 𝑇𝑇)𝑐𝑐 = 𝑆𝑆 𝑐𝑐 ∩ 𝑇𝑇 𝑐𝑐 . Use a diagram to see the intuition.
Question 2.19. Prove 𝑓𝑓 −1 (𝐴𝐴 ∪ 𝐵𝐵) = 𝑓𝑓 −1 (𝐴𝐴) ∪ 𝑓𝑓 −1 (𝐵𝐵) and 𝑓𝑓 −1 (𝐴𝐴 ∩ 𝐵𝐵) = 𝑓𝑓 −1 (𝐴𝐴) ∩ 𝑓𝑓 −1 (𝐵𝐵).
Question 2.20. Prove the Euler Law.
Question 2.21. Prove the second proposition on homogeneity (Proposition 2.9).
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