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Section 1.4

Section 1.4. Comparing Sets. Objectives. Recognize equivalent sets. Recognize equal sets. Recognize subsets and use the notation . Recognize proper subsets and use the notation . Determine the number of subsets of a set. . Key Terms.

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Section 1.4

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  1. Section 1.4 Comparing Sets

  2. Objectives Recognize equivalent sets. Recognize equal sets. Recognize subsets and use the notation . Recognize proper subsets and use the notation . Determine the number of subsets of a set.

  3. Key Terms Equal: Set A is equal to Set B iff they contain exactly the same elements, regardless of order or possible repetition of elements, symbolized by A = B. Equivalent: sets are said to be equivalent if they contain the same number of elements, and the elements can be placed in a one-to-one correspondence. Subset: Set A is a subset of Set B, symbolized by A B, iff all the elements of Set A are also elements of Set B. Proper Subset: Set A is a proper subset of Set B, symbolized by A B, iff all the elements of Set A are elements of Set B and Set A ≠ Set B (Set B has to be larger).

  4. **Special Note: All equalsets are equivalent, but all equivalent sets are not equal.

  5. Example 1: Equal Sets – exactly the same elements Decide whether each pair of sets is equal. {1, 3, 5, 7, 9} and {1, 5, 9, 3, 7} {x/x is a counting number between 5 and 19 inclusive} {y/y is a rational number between 5 and 19 inclusive}

  6. Example 2: Equivalent Sets – exactly the same number of elements Decide whether each set is equivalent {1, 2, 3, 4, 5} and {a, e, i, o, u} {x/x is a letter in the world tenacity} and {x/x is a letter in the word resolve}

  7. Example 3: Subsets List all the subsets. {1, 2, 3} {a, b, c, d} Formula:

  8. Example 4: Subset/Not A Subset {2, 3, 7} ______{1, 2, 3, 4, 5, 6, 7} {-4, 0, 4} ______{-4, -3, -2, -1, 1, 3, 4} {x/x is a dog} ______{x/x is a pure bred dog}

  9. Example 5: Proper Subsets List all the Proper Subsets. {1, 3, 4, 7, 9} {a, c, e, g} Formula:

  10. Section 1.4 Assignment • Classwork: • TB pg. 36/2 – 30 Even • Must write problemsand show ALL answers to receive credit for this assignment. • Homework:

  11. Example 6: Subsets • List all the two element subsets: • {1, 2, 3, 4, 5} • List all the three element subsets: • {a, b, c, d, e, f}

  12. Example 7: Consider the following sets: U = (Upperclassmen); L = (Lowerclassmen); S (Science Majors); V (GPA above 3.0); A (Art Majors); T (Athletes); and D (involved in Drama). Find a set that is equal to V.

  13. Example 8: Consider the following sets: U = (Upperclassmen); L = (Lowerclassmen); S (Science Majors); V (GPA above 3.0); A (Art Majors); T (Athletes); and D (involved in Drama). Find a set whose cardinal number is the largest of all the sets.

  14. Example 9: • TB pg. 33/Example 3

  15. Section 1.4 Assignments • Classwork: • TB pg. 36/31 – 34, 39 – 46, and 51 and 52 • Must write problems and show ALL answers to receive credit for this assignment. • Homework:

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