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# Set

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### Set

1. 1. SETSA = {1, 3, 2, 5}n(A) = | A | = 4Sets use “curly” bracketsThe number of elementsin Set A is 4Sets are denoted byCapital lettersA3∈A7∉3 is an element of A7 is not an element of A
2. 2. A set is a distinct collection of objects. The objects arecalled elements.{1, 2, 3, 4} = {2, 3, 1, 4}Order does not matter. If a setcontains the same elements asanother set, the sets are equal.{1, 3, 2, 3, 5, 2} We never repeat elements in a set.{1, 3, 2, 5}This symbol means "is a subset of"This is read "A is a subset of B".A ⊂ BA = {1, 2, 3} B = {1, 2, 3, 4, 5}{1, 2, 3, 5} In ascending order
3. 3. If a set doesnt contain any elements it is called theempty set or the null set. It is denoted by ∅ or { }.NOT {∅} It is agreed that the empty set is a subset of all other setsso:where is any set.A A∅ ⊆List all of the subsets of {1, 2, 3}.∅Notice the emptyset is NOT in setbrackets.{1} {2} {3} {1, 2} {1, 3} {2, 3} {1, 2, 3}A⊂∅
4. 4. ?Number ofElements in SetPossible Subsets Total Number ofPossible Subsets1. {A} {A} ∅ 22. {A , B} {A , B} {A} {B} ∅ 43. {A , B , C} {A , B , C} {A , B} {A , C}{B , C} {A} {B} {C}∅84. {A , B , C, D} {A , B , C , D} {A , B , C}{A , B , D} {A , C , D}{B , C , D} {A , B} {A , C}{A , D} {A , B} …… {D} ∅16The number of possible subsets of a set of size n is ?2n
5. 5. A ∪ BThis is the union symbol. It means the set that consists of allelements of set A and all elements of set B.= {1, 2, 3, 4, 5, 7, 9}Remember we donot list elementsmore than once.A ∩ BThis is the intersect symbol. It means the setcontaining all elements that are in both A and B.= {1, 3, 5}A = {1, 2, 3, 4, 5} B = {1, 3, 5, 7,9}
6. 6. These sets can be visualized with circles in what is called aVenn Diagram.A ∪ BA BEverything that is inA or B.A BA ∩ BEverything that is inA AND B.A B
7. 7. Often will have a set that contains all elements that wewish to consider. This is called the universal set. All othersets are subsets of this set.Universal SetA BA ∩ B = ∅There are noelements inboth A and B.When this isthe case theyare calleddisjoint sets.AThis means the complement of A, andmeans the set of all elements in theuniversal set that are not in A.A A
8. 8. 100 people were surveyed. 52 people in a survey owned acat. 36 people owned a dog. 24 did not own a dog or cat.Draw a Venn diagram.universal set is 100 people surveyedC DSet C is the cat owners and Set D is the dogowners. The sets are NOT disjoint. Somepeople could own both a dog and a cat.24Since 24did not owna dog orcat, theremust be 76that do.n(C ∪ D) = 76This n means thenumber of elementsin the set52 + 36 = 88 sothere must be88 - 76 = 12people that ownboth a dog anda cat.1240 24Counting Formula:n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
9. 9. AcknowledgementI wish to thank Shawna Haider from Salt Lake Community College, UtahUSA for her hard work in creating this PowerPoint.www.slcc.eduShawna has kindly given permission for this resource to be downloadedfrom www.mathxtc.com and for it to be modified to suit the WesternAustralian Mathematics Curriculum.Stephen CorcoranHead of MathematicsSt Stephen’s School – Carramarwww.ststephens.wa.edu.au
10. 10. AcknowledgementI wish to thank Shawna Haider from Salt Lake Community College, UtahUSA for her hard work in creating this PowerPoint.www.slcc.eduShawna has kindly given permission for this resource to be downloadedfrom www.mathxtc.com and for it to be modified to suit the WesternAustralian Mathematics Curriculum.Stephen CorcoranHead of MathematicsSt Stephen’s School – Carramarwww.ststephens.wa.edu.au