1 / 19

SET THEORY

SET THEORY. A Brief Introduction. Let’s Begin with an Activity. Anie and Jessi eat croissants every morning. Anie , Jessi , and Lauren all love Artemis!. Partner up with 2 of your neighbors

adelie
Télécharger la présentation

SET THEORY

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. SET THEORY A Brief Introduction

  2. Let’s Begin with an Activity Anie and Jessi eat croissants every morning Anie, Jessi, and Lauren all love Artemis! • Partner up with 2 of your neighbors • Find out your similarities and differences. (Do you all like chocolate ice cream? Have you read Harry Potter? Etc…) • Fill in each section of the Venn Diagram

  3. What is a Set? • A set is a collection of distinct objects. • Example: {Book, Chair, Pen} • In a set, order does not matter • Example: {Book, Chair, Pen} = {Pen, Book, Chair} • Duplicates do not alter the set • Example: {NickiMinaj, Drake, Drake} = {NickiMinaj, Drake}

  4. Two Important Sets • Empty (Null) Set: A set with no elements • Denoted by  or {} • Universal Set: A set that contains all objects in the universe • Denoted by Ω

  5. Elements • The objects in a set are called “elements” • Let S = {Ajja, Frannie, Julia} • Ajjais “an element of” set S because she is part of that set • The shorthand notation for this is ’∈’ “ Ajja∈ S ” translates to “Ajjais an element of set S”

  6. Basic Operations • Union: The union of 2 sets is all the elements that are in both sets • Denoted by ‘U’ • Example: Let A={1,2,3} and B={1,4,5} • A U B= {1, 2, 3, 4, 5}

  7. Basic Operations • Intersection: The intersection of 2 sets is the set of elements they have in common (think of the overlapping parts of the Venn diagram) • Denoted by ‘∩’ • Example: Let A={1,2,3} and B={1,4,5} • A ∩ B = {1}

  8. Basic Operations • Set Difference: The set of elements in one set and not the other • Denoted by ‘\’ • Example: Let A={1,2,3} and B={1,4,5} • A\B = {2, 3}

  9. Back to your Venn Diagram • Identify … • the union • the intersection • the set difference

  10. Solutions: Union

  11. Solutions: Intersection

  12. Solutions: Set Difference

  13. Why is Set Theory Important? • True Algebra is the study of sets and operations on those sets • The idea of grouping objects is really useful • Examples: Complexity Theory: Branch in CS that focuses on classifying problems by difficulty. • Problems are sorted into different sets based on how hard they are to solve The formal, mathematical definition of Probability is defined in terms of sets

  14. SET: The Game • Rules • Each card is unique in 4 characteristics: color, shape, number, and shading • 3 cards form a SET if each characteristic is the same for all cards or different for all cards • Yell SET to claim cards • Player with the most SETs wins

  15. This is a SET COLOR: ALL red SHAPE: ALL ovals NUMBER: ALL twos SHADING: ALL different

  16. This is NOT a SET SHAPE: ALL Squiggly NUMBER: ALL twos SHADING: ALL different COLOR: NOT ALL red  NOT a SET

  17. Yes Is this a SET? SHAPE: ALL different NUMBER: ALL different SHADING: ALL striped COLOR: ALL different

  18. No Is this a SET? Magic Rule: If two are _______ and one is not, then it is not a SET SHAPE: ALL diamonds NUMBER: ALL ones COLOR: ALL different SHADING: NOT ALL hollow

  19. Let’s Play!

More Related