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.