Set Properties

• Read carefully pages 111 through 114 (sections 4.5, 4.6)
• Some key questions to answer (try these without looking at the book, but after you’ve read the book):
  1. State and prove the distributive laws for sets.
  2. State and prove De Morgan’s laws for sets.
  3. Prove that if \(A\) is a subset of \(B\) and \(C\) is a subset of \(D\), then \(A\times C\) is a subset of \(B\times D\).
  4. For sets \(A\), \(B\), \(C\) show that \((A\cup B)\times C\) is equal to \((A\times C)\cup (B\times C)\).
  5. For sets \(A\), \(B\), \(C\) show that \(A\times (B\setminus C)\) is equal to \((A\times B)\setminus (A\times C)\).
  6. For sets \(A\), \(B\), \(C\), how do \(A\times(B\cap C)\) and \((A\times B)\cap (A\times C)\) compare?
• Practice problems from section 4.5 (page 116): 4.53, 4.55, 4.57, 4.59
• Practice problems from section 4.6 (page 116): 4.63, 4.64, 4.65, 4.67