LMS-Week-3.1-MATH-1013-Set-Operations

Week Overview

  • Topics covered: Set Operations, Applications in Mathematics

Learning Outcomes

  • Students will be able to:

    • Perform set operations: union, intersection, complement, difference.

    • Use proper notation for set operations.

    • Apply set operations to solve mathematical problems.

Introduction to Sets

  • Definition: A set is a collection of distinct objects or elements.

  • Example: Let U = {x | x is a Korean drama series}.

Examples of Sets in Context

  • Nominees for Best Drama Series (Baeksang Arts Awards)

    • Set A = {Hot Stove League, When the Camellia Blooms, Crash Landing on You, Kingdom 2, Hyena}

  • Nominees for Best Drama Miniseries (Seoul International Drama Awards)

    • Set B = {Hot Stove League, When the Camellia Blooms, Crash Landing on You, Kingdom 1, Itaewon Class}

  • Top Rated Dramas (2019-2020)

    • Set C = {Hospital Playlist, Crash Landing on You, The King: Eternal Monarch, Dinner Mate, Kingdom 1}

  • Common Elements: Some dramas appear in more than one category.

    • Intersection of A and B: {Hot Stove League, When the Camellia Blooms, Crash Landing on You}.

Set Operations

Intersection of Sets

  • Definition: A ∩ B is the set of elements that are in both set A and set B.

    • Example: A ∩ B = {Hot Stove League, When the Camellia Blooms, Crash Landing on You}.

    • Notation: A ∩ C = {Crash Landing on You}, B ∩ C = {Crash Landing on You, Kingdom 1}.

Union of Sets

  • Definition: A U B is the true larger set formed from all elements of A and B.

    • Example: A U B = {Hot Stove League, When the Camellia Blooms, Crash Landing on You, Kingdom 1, Itaewon Class, Kingdom 2, Hyena}.

    • Notation for larger unions:

      • A U C = {Hot Stove League, When the Camellia Blooms, Crash Landing on You, Kingdom 2, Hyena, Hospital Playlist, The King: Eternal Monarch, Dinner Mate, Kingdom 1}.

Universal Set

  • Definition: The universal set is the set that contains all elements relevant to a particular discussion or problem.

    • Example: U = {0,1,2,3,4,5,6,7,8,9}.

Additional Set Operations

Difference of Sets

  • Definition: A - B is the set of all elements in A that are not in B.

    • Examples:

      • Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {4,5,7}, B = {6,7}.

      • U - A = {0, 1, 2, 3, 6, 8, 9}.

Complement of Sets

  • Definition: The complement of set A, denoted A', consists of all elements in U that are not in A.

    • Example: A = {2,4,6,8}.

      • A' = {0,1,3,5,7,9}.

Disjoint Sets

  • Definition: Two sets are disjoint if they have no elements in common (i.e., their intersection is empty).

    • Example: A ∩ C for specific sets yields an empty result.

Practice Exercises

  • Example Problems with sets to reinforce concepts including:

    1. B - C

    2. A - B

    3. B - (C - A).

Thank You

  • Appreciation for participating in the class.

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