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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

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SET THEORY

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  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!

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