Miscellaneous Set Concepts Slides to accompany Sections 1.(8 & 9) - PowerPoint PPT Presentation

Miscellaneous Set Concepts Slides to accompany Sections 1.(8 & 9) of Discrete Mathematics and Functional Programming Thomas VanDrunen

Tree example T SugarMaple SilverMaple BoxElder BaldCypress PinOak WhitePine LiveOak BristleconePine | I | = 6 .

Tree example T SugarMaple SilverMaple A BoxElder BaldCypress PinOak WhitePine LiveOak BristleconePine C | I | = 6 .

Tree example T SugarMaple SilverMaple D BoxElder BaldCypress PinOak WhitePine LiveOak E BristleconePine | I | = 6 .

Tree example T SugarMaple SilverMaple BoxElder BaldCypress PinOak I WhitePine LiveOak BristleconePine | I | = 6 .

Tree example T M SugarMaple SilverMaple BoxElder BaldCypress X PinOak WhitePine LiveOak BristleconePine Q P | I | = 6 .

Cardinality T SugarMaple SilverMaple BoxElder BaldCypress X PinOak I WhitePine LiveOak E BristleconePine | I | = 6 . | X | = 1 . | E | = 3 . | I − E | = 5 . | X − I | = 0 .

Disjoint T M SugarMaple SilverMaple BoxElder BaldCypress PinOak WhitePine LiveOak E BristleconePine M ∩ E = ∅ . | M ∩ E | = 0 .

Not Disjoint T SugarMaple SilverMaple D A BoxElder BaldCypress PinOak WhitePine LiveOak E BristleconePine C A ∩ E = { LiveOak } � = ∅ . C ∩ D = { BaldCypress } � = ∅ .

Pairwise disjoint T M SugarMaple SilverMaple BoxElder BaldCypress X PinOak WhitePine LiveOak BristleconePine Q P | I | = 6 .

Questions ( E − C ) ∩ ( C − E ) = ( { LiveOak , WhitePine , BristleconePine } −{ WhitePine , BristleconePineBaldCypress } ) ∩{ WhitePine , BristleconePineBaldCypress } − ( { LiveOak , WhitePine , BristleconePine } ) = { LiveOak } ∩ { BaldCypress } ∅ = Is it true that for any two sets A and B , ( A − B ) ∩ ( B − A ) = ∅ ?

Questions | M ∪ Q | |{ SugarMaple , SilverMaple , BoxElder } = ∪{ PinOak , LiveOak }| |{ SugarMaple , SilverMaple , BoxElder , = PinOak , LiveOak }| = 5 = 3 + 2 = |{ SugarMaple , SilverMaple , BoxElder }| + |{ PinOak , LiveOak }| = | M | + | Q | Is it true that for any two sets A and B , | A ∪ B | = | A | + | B | ?

Questions | C − X | = |{ WhitePine , BristleconePine , BaldCypress } −{ BaldCypress }| = |{ WhitePine , BristleconePine }| = 2 = 3 − 1 = |{ WhitePine , BristleconePine , BaldCypress }| −|{ BaldCypress }| | C | − | X | = Is it true that for any two sets A and B , | A − B | = | A | − | B | ?

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane

Cartesian Plane (8.6, 5.5)

Cartesian product Real (Cartesian) plane R × R = { ( x , y ) | x , y ∈ R } Cartesian product of sets X and Y : X × Y = { ( x , y ) | x ∈ X and y ∈ Y } (The set of ordered pairs drawn from X and Y .)