Subsets

• Read pages 18 through 21 (section 1.2)
• Some key questions to answer:
  1. When do we say that a set \(A\) is a subset of another set \(B\)? How do we denote that?
  2. Is a set a subset of itself?
  3. Explain in precise terms why if \(A\) is a subset of \(B\) and \(B\) is a subset of \(C\), then \(A\) must be a subset of \(C\).
  4. Study example 1.5 carefully, make sure you understand it, and produce another example of it.
  5. True or False: For any two sets \(A\), \(B\), we must have either that \(A\) is a subset of \(B\) and that \(B\) is a subset of \(A\) (or both).
  6. How do we denote that a set is not a subset of another set?
  7. True or False: If \(A\) is not a subset of \(B\), then none of the elements of \(A\) are in \(B\).
  8. Is there a set that is a subset of all other sets?
  9. Does the empty set have any subsets?
  10. What is the meaning of a “universal set”?
  11. List the various kinds of intervals and write them both in interval notation and in set notation.
  12. When do we say that \(A\) is a “proper subset” of \(B\)?
  13. Is there a set without any proper subsets?
  14. What is the “powerset” of a set \(A\)?
• Practice problems from section 1.2 (page 31): 1.10, 1.11, 1.13, 1.17, 1.19