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AND. Chapter 2. Sets. • Methods to indicate sets, equal sets, and equivalent sets • Subsets and proper subsets • Venn diagrams • Set operations such as complement, intersection, union, difference and Cartesian product • Equality of sets • Application of sets • Infinite sets.

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  1. AND

  2. Chapter 2 Sets

  3. • Methods to indicate sets, equal sets, and equivalent sets • Subsets and proper subsets • Venn diagrams • Set operations such as complement, intersection, union, difference and Cartesian product • Equality of sets • Application of sets • Infinite sets WHAT YOU WILL LEARN

  4. Section 2 Subsets

  5. Subsets

  6. Í A B . Determining Subsets Example: Determine whether set A is a subset of set B. A = { 3, 5, 6, 8 } B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Solution: All of the elements of set A are contained in set B, so

  7. Proper Subset

  8. Determining Proper Subsets Example: Determine whether set A is a proper subset of set B. A = { dog, cat } B = { dog, cat, bird, fish } Solution: All the elements of set A are contained in set B, and sets A and B are not equal, therefore AB.

  9. Determining Proper Subsets (continued) Example: Determine whether set A is a proper subset of set B. A = { dog, bird, fish, cat } B = { dog, cat, bird, fish } Solution: All the elements of set A are contained in set B, but sets A and B are equal, therefore AB.

  10. Number of Distinct Subsets • The number of distinct subsets of a finite set A is 2n, where n is the number of elements in set A. Example: • Determine the number of distinct subsets for the given set { t , a , p , e }. • List all the distinct subsets for the given set: { t , a , p , e }.

  11. Number of Distinct Subsets continued Solution: • Since there are 4 elements in the given set, the number of distinct subsets is 24 = 2 • 2 • 2 • 2 = 16 subsets. • {t,a,p,e}, {t,a,p}, {t,a,e}, {t,p,e}, {a,p,e}, {t,a}, {t,p}, {t,e}, {a,p}, {a,e}, {p,e}, {t}, {a}, {p}, {e}, { }

  12. CourseSmart Page 58

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