2.3 ­ Venn Diagrams and Set .2.3 ­ Venn Diagrams and Set Operations ­ 2nd hour

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September04,2015

2.3VennDiagramsandSetOperations

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TERMINOLOGY

VennDiagramArectanglerepresentingtheuniversalset,U,wheretheitemsinsidetherectanglemaybedividedintosubsetsoftheuniversalset

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THEFOURTYPESOFSUBSETSINVENNDIAGRAMS

CASE1:DisjointSets

CASE2:Subsets

CASE3:EqualSets

CASE4:OverlappingSets

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KEYCONCEPTSThecomplimentofsetA,symbolizedbyA',isthesetofalltheelementsintheuniversalsetthatarenotinsetA

TheintersectionofsetsAandB,symbolizedbyA B,isthesetcontainingalltheelementsthatarecommontobothsetAandsetB.

TheunionofsetsAandB,symbolizedbyA B,isthesetcontainingalltheelementsthataremembersofSetAorofSetB,orofbothsets.

ThewordORmeansunionandthewordANDmeansintersection.

n(A B) = n(A) + n(B) - n(A B)

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Example1:ASetandItsComplimentGivenU={x|0

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Example2:Lettheuniversalset,U,representthesetofallUScorporationsin2001.LetSetArepresentthe10largestUScorporationsin2001andletsetBrepresentthesetofthe10leadingadvertisers.DrawaVenndiagramillustratingtherelationshipbetweensetAandsetB.

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Example3:Given:U={1,2,3,4,5,6,7,8,9,10},A={1,2,4,6},B={1,3,6,7,9},andC={},findthefollowing:

a)A B

b)A C

c)A' B

d)(A B)'

e)A B

f)A C

g)A' B

h)(A B)'

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Example4:UsetheVennDiagramtofindthefollowing

a)U

b)A

c)B'

d)A B

e)A B

f)(A B)'

g)n(A B)

U A B

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Example5:GivenU={a,b,c,d,e,f,g},A={a,b,e,g},B={a,c,d,e}andC={b,e,f}findthefollowing:

a)(AB)(AC)

b)(AB)C'

c)A'B'

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Example6:TheresultsofasurveyofvisitorsattheGrandCanyonshowedthat25speakSpanish,14speakFrench,and4speakbothSpanishandFrench.HowmanyspeakSpanishorFrench?

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Example7:SetAcontains6lettersand5numbers.SetBcontains4lettersand9numbers.Twolettersand1numberarecommontobothsetsAandB.FindthenumberofelementsinsetAorsetB.

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HOMEWORK

Page 1: Sep 3-1:05 PMPage 2: Sep 3-1:05 PMPage 3: Sep 3-1:05 PMPage 4: Sep 3-1:05 PMPage 5: Sep 3-1:43 PMPage 6: Sep 3-1:05 PMPage 7: Sep 3-1:05 PMPage 8: Sep 3-1:05 PMPage 9: Sep 3-1:05 PMPage 10: Sep 3-1:05 PMPage 11: Sep 3-1:05 PMPage 12: Sep 3-1:05 PMPage 13: Sep 3-1:05 PM