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12-8

Set Theory. 12-8. Course 2. Warm Up. Problem of the Day. Lesson Presentation. Set Theory. 12-8. Course 2. Warm Up Tell in which intervals of x the graph shows constant rates of change. from x = 0 to x = 2, x =2 to x = 4, x = 4 to x = 5, and x = 5 to x = 9. Set Theory.

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12-8

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  1. Set Theory 12-8 Course 2 Warm Up Problem of the Day Lesson Presentation

  2. Set Theory 12-8 Course 2 Warm Up Tell in which intervals of x the graph shows constant rates of change. from x = 0 to x = 2, x =2 to x = 4, x = 4 to x = 5, and x = 5 to x = 9

  3. Set Theory 12-8 Course 2 Problem of the Day What is the intersection of the set of all prime numbers and the set of all even numbers? 2

  4. Set Theory 12-8 Course 2 Learn to use set notation and to identify relationships between sets.

  5. Set Theory 12-8 Course 2 Insert Lesson Title Here Vocabulary set element

  6. Set Theory 12-8 Course 2 The states that are bordered by the Pacific Ocean for a set. The set of states in the United States that are bordered by the Pacific Ocean includes California, Oregon, Washington, Alaska, and Hawaii. A setis a collection of objects. Each object in a set is an elementof the set. The special set that contains no elements is the null set, or empty set. When describing sets using symbols, you can use either roster notation or set-builder notation.

  7. Set Theory 12-8 Course 2 {x|x is a state that is bordered by the Pacific Ocean} {CA, OR, WA, AK, HI} Roster notation lists all of the elements. Set-builder notation gives a rule. Reading Math Read the notation {x|x is a real number} as “the set of all x such that x is a real number.”

  8. Set Theory 12-8 Course 2 Additional Example 1: Writing in Set Notation Write each set using roster notation or set builder notation. A. the set of all positive multiples of 3 less than or equal to 15 The numbers can be listed conveniently. Use roster notation. {3, 6, 9, 12, 15} B. the set of all multiples of 3 The numbers follow a rule but cannot all be listed conveniently. Use set-builder notation. {x|x is a multiple of 3}

  9. Set Theory 12-8 Course 2 Insert Lesson Title Here Try This: Example 1 Write each set using roster notation or set builder notation. A. the set of all odd numbers from 1 to 10, including 1 The numbers can be listed conveniently. Use roster notation. {1, 3, 5, 7, 9} B. the set of all odd integers greater than zero The numbers follow a rule but cannot all be listed conveniently. Use set-builder notation. {x|x is an odd counting number}

  10. Set Theory 12-8 Course 2 The following notations show how different sets can relate to each other.

  11. Set Theory 12-8 Course 2

  12. Set Theory 12-8 Course 2

  13. Set Theory 12-8 Course 2 Additional Example 2A: Identifying Relationships Between Sets Find A B and A  B. Tell whether A  B, B  A,or neither. A. A = {0, 5, 10}; B = {1, 2, 3, 4, 5} A  B = {5} 5 is in both A and B. A  B = {0, 1, 2, 3, 4, 5, 10} List the members of both sets. Neither set is a subset of the other.

  14. Set Theory 12-8 Course 2 Additional Example 2B: Identifying Relationships Between Sets Find A  B and A  B. Tell whether A  B, B  A,or neither. B. A = {1, 2, 3}; B = {1, 2, 3, 4, 5} 1, 2, and 3 in both A and B. A  B = {1, 2, 3} List the members of both sets. A B = {1, 2, 3, 4, 5} All the members of A are in B. A B

  15. Set Theory 12-8 Course 2 Additional Example 2C: Identifying Relationships Between Sets Find A  B and A  B. Tell whether A  B, B  A,or neither. C. A = {x|x is an even integer}; B = {x|x is an odd integer} No number is both even and odd. A B = { } = Ø Together, the set of even integers and the set of odd integers make up the set of integers. AB = {x|x is an integer} Neither set is a subset of the other.

  16. Set Theory 12-8 Course 2 Try This: Example 2A Find A B and A  B. Tell whether A  B, B  A,or neither. A. A = {0, 1, 2}; B = {2, 3, 4, 5} 2 is in both A and B. A  B = {2} A  B = {0, 1, 2, 3, 4, 5} List the members of both sets. Neither set is a subset of the other.

  17. Set Theory 12-8 Course 2 Try This: Example 2B Find A  B and A  B. Tell whether A  B, B  A,or neither. B. A = {4, 5}; B = {1, 2, 3, 4, 5, 6} 4 and 5 are in both A and B. A  B = {4, 5} List the members of both sets. A B = {1, 2, 3, 4, 5, 6} All the members of A are in B. A B

  18. Set Theory 12-8 Course 2 Additional Example 2C: Identifying Relationships Between Sets Find A  B and A  B. Tell whether A  B, B  A,or neither. C. A = {x|x is an even integer}; B = {x|x is an irrational number} No number is both an integer and irrational. A B = { } = Ø List the members of both sets. AB = {x|x is an even integer or an irrational number} Neither set is a subset of the other.

  19. Set Theory 12-8 Course 2 Insert Lesson Title Here Lesson Quiz: Part 1 Write each set using roster notation or set-builder notation. 1. The set of positive multiples of 4 less than 24 2. The set of all state capitals. {4, 8, 12, 16, 20} {x|x is the capital of a state}

  20. Set Theory 12-8 Course 2 Insert Lesson Title Here Lesson Quiz: Part 2 Find A B and A  B and tell whether one set is a subset of the other. 3.A = {–8, –10, –12, –14} and B = {–8, –12, –16} 2.A = {whole numbers} and B = {3, 5, 7, 9, 12} A  B = {–8, –10, –12, –14, –16} A B = {–8, –12}; neither is a subset of the other. AB = {whole numbers} A B = {3, 5, 7, 9, 12}; B  A

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