Topics covered: Set Operations, Applications in Mathematics
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.
Definition: A set is a collection of distinct objects or elements.
Example: Let U = {x | x is a Korean drama series}.
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}.
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}.
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}.
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}.
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}.
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}.
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.
Example Problems with sets to reinforce concepts including:
B - C
A - B
B - (C - A).
Appreciation for participating in the class.