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Discrete Mathematics

Discrete Mathematics. 5.01-Set Concepts ST 1. Objectives: Students will…. classify sets. represent sets with set-builder and roster methods. compare sets. Vocabulary. set – a collection of objects members or elements – the objects in a set

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Discrete Mathematics

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  1. Discrete Mathematics 5.01-Set Concepts ST 1

  2. Objectives: Students will… • classify sets. • represent sets with set-builder and roster methods. • compare sets.

  3. Vocabulary • set – a collection of objects • members or elements – the objects in a set • well-defined set – when elements are clearly determined (no opinion just facts).

  4. Three methods to describe a set: • Description: using words • Roster Form: Elements are listed in braces and separated by a comma. • Set-Builder notation: Set A All x’s must meet this condition Such that The set of All values of x

  5. Description Method • Write a description for the set Patrick, Sandy, Mr. Krabs, Gary, Pearl, Squidward, Plankton, Mrs. Puff, and Spongebob. • Answer: The set of main characters on Spongebob Squarepants.

  6. You Try • Write a description for the set Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. • Answer: The set of the days of the week.

  7. Roster Method • Express the following in roster form: Set G is the set of Classic Crayola Crayons. • Answer: G= {brown, red, orange, yellow, green, blue, purple, black}

  8. You Try #1 • Express the following in roster form: Set P is the set of planets in Earth’s solar system. • Answer: P= {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune} *as of August 2006, Pluto was reclassified

  9. You Try #2 • Set A is the set of natural ( aka counting) numbers greater than 5. • Answer: A= {6, 7, 8, 9, 10, …} ellipsis tell us that the set continues in the same manner.

  10. Set-Builder Notation (AKA set notation) • Write the set G= {January, February, March, April, May, June, July, August, September, October, November, December} using set-builder notation. • Answer:

  11. Another Example • Write set B= {1, 2, 3, 4, 5} in set-builder notation. • Answer: “ is an element of ” The opposite symbol means “ is not an element of.”

  12. You Try • Write set B= {2, 3, 4, 5, 6, 7} in set-builder notation. • Answer:

  13. Inclusive • Inclusive means that you include the end values. • Ex: Put the following in roster form: • The set of natural numbers between 4 and 9 A = {5, 6, 7, 8} VERSUS • The set of natural numbers between 4 and 9, inclusive A = {4, 5, 6, 7, 8, 9} • Ex: Put the following in set builder notation: • Set A is the natural numbers between 7 and 12. VERSUS • The natural numbers between 7 and 12, inclusive.

  14. Cardinal Number • The cardinal number, symbolized by n(A), is the number of elements in set A. • Example: Find n(B) if B= {11, 34, 49, 101}. • Answer: n(B) = 4

  15. Equal Versus Equivalent • Equal sets: Sets containing exactly the same elements. Order does not matter. Notation: A = B • Equivalent Sets: Sets containing the same number of elements. Notation: n(A) = n(B)

  16. Finite Versus Infinite • Finite Set: A set with no elements or with a number of elements that can be represented with a natural number. • Infinite Set: A set with a number of elements that cannot be counted. Notation: A = {1, 2, 3, …}

  17. Empty Versus Universal • Empty or Null Set: A set containing no elements. Notation: { } or • Universal Set: A set that contains all the elements for any specific discussion Notation:

  18. Assignment • Worksheet 5.01

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