92 CHAPTER 2 Sets Important Facts and Concepts Examples and Discussion Section 2.3 Symbol Meaning ′ complement ù intersection ø union − difference of two sets × Cartesian product And is generally interpreted to mean intersection. Or is generally interpreted to mean union. For any sets A and B, = + − nAB nAnB nAB ( ) ( ) ( ) ( ) ø ù Examples 1, 4, 6–8, 11, pages 59–61, 62–66 Examples 2–4, 6–8, pages 60–61, 62–64 Examples 5–8, pages 63–64 Example 11, page 66 Example 12, page 67 Examples 9 and 10, page 63 Examples 9 and 10, page 63 Section 2.4 De Morgan’s Laws ′ = ′ ′ ′ = ′ ′ A B A B A B A B ( ) ( ) ù ø ø ù Example 3, page 74 Section 2.6 An infinite set is a set that can be placed in a one-to-one correspondence with a proper subset of itself. ℵ0 is read aleph-null Countable sets Examples 1–5, pages 88–90, Discussion page 87 Examples 4–5, pages 89–90 Examples 4–5, pages 89–90 Review Exercises CHAPTER 2 2.1, 2.2, 2.3, 2.4, 2.6 In Exercises 1–14, state whether each statement is true or false. If false, give a reason. 1. The set of stores located in the state of Wyoming is a welldefined set. True 2. The set of the three best songs is a well-defined set. False; the word best makes the statement not well defined. 3. ∈ maple {oak, elm, maple, sycamore} True 4. ∅ {} , False; no set is a proper subset of itself. 5. … {3, 6, 9, 12, } and … {2, 4, 6, 8, } are disjoint sets. False; the elements 6, 12, 18, 24, … are members of both sets. 6. {Mercury, Venus, Earth, Mars} is an example of a set in roster form. True 7. = {candle, picture, lamp} {picture, chair, lamp} False; the sets do not contain the same elements. 8. {apple, orange, banana, pear} is equivalent to {tomato, corn, spinach, radish}. True 9. = = A n A If {pen, pencil, book, calculator}, then ( ) 4.True 10. = … A {1, 3, 5, 7, } is a countable set. True 11. A {1, 4, 7, 10, , 31} = … is a finite set. True 12. {2, 5, 7} {2, 5, 7, 10}. # True 13. | ∈ < ≤ x x N x { and 3 9} is a set in set-builder notation. True 14. | ∈ < ≤ … x x N x { and 2 12} {1, 2, 3, 4, 5, , 20} # True In Exercises 15–18, express each set in roster form. 15. Set A is the set of odd natural numbers between 5 and 16. = A {7, 9, 11, 13, 15}
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