MAT 142 Lecture Video SeriesApplications of Venn DiagramsObjectivesA survey of 300 workers yielded the following information: 231 belonged to a union, and 195 were Democrats. If 172 of the union members were Democrats, how many workers were in the following situations?Slide 5A consumer survey was conducted to examine the patterns in ownership of personal computers, cellular phones, and VCRs. The following data were obtained: 1308 had personal computers, 962 had cellular phones, 1298 had VCRs, 172 had all three, 289 had none, 339 had cell phones and VCRs, 351 had cell phones but no computers or VCRs, and 136 had computers and VCRS but no cell phones.Slide 7A recent transportation survey of w urban commuters (that is n(U) = w) yielded the following information: x rode neither trains nor busses, y rode trains, and z rode only trains. How many people rode the following?Slide 9Slide 10Given the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {0, 2, 4, 5, 9}, and B = {1, 2, 7, 8, 9} use DeMorgan’s laws to find:A nonprofit organization’s board of directors, composed of four women (Angela, Betty, Carmine, and Delores) and three men (Ed, Frank, and Grant), holds frequent meetings. A meeting can be held at Betty’s house, at Delores’s house, or at Frank’s house.RestrictionsCreator and Producer Elizabeth Jones for The School of Mathematical and Statistical Sciences at Arizona State University Videographer Mike Jones ©2009 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State UniversityMAT 142Lecture Video SeriesApplications of Venn DiagramsObjectives•Use Venn diagrams to answer questions about survey results. •Apply De Morgan’s laws to find complements of unions and intersections. •Solve logic problems.A survey of 300 workers yielded the following information:( 231 belonged to a union, and 195 were Democrats.( If 172 of the union members were Democrats, how many workers were in the following situations? •belonged to a union or were Democrats•belonged to a union but were not DemocratsA survey of 300 workers yielded the following information:( 231 belonged to a union, and 195 were Democrats.( If 172 of the union members were Democrats, how many workers were in the following situations? •were Democrats but did not belong to a union •neither belonged to a union nor were DemocratsA consumer survey was conducted to examine the patterns in ownership of personal computers, cellular phones, and VCRs. The following data were obtained: 1308 had personal computers, 962 had cellular phones, 1298 had VCRs, 172 had all three, 289 had none, 339 had cell phones and VCRs, 351 had cell phones but no computers or VCRs, and 136 had computers and VCRS but no cell phones.•What percent of the people surveyed owned a cell phone?A consumer survey was conducted to examine the patterns in ownership of personal computers, cellular phones, and VCRs. The following data were obtained: 1308 had personal computers, 962 had cellular phones, 1298 had VCRs, 172 had all three, 289 had none, 339 had cell phones and VCRs, 351 had cell phones but no computers or VCRs, and 136 had computers and VCRS but no cell phones.•What percent of the people surveyed owned only a cell phone?A recent transportation survey of w urban commuters (that is n(U) = w) yielded the following information:( x rode neither trains nor busses, y rode trains, and z rode only trains.( How many people rode the following? •trains and busses •only bussesA recent transportation survey of w urban commuters (that is n(U) = w) yielded the following information:( x rode neither trains nor busses, y rode trains, and z rode only trains.( How many people rode the following? •busses •trains or bussesDeMorgan’s Laws (for sets)Formulas BABA BABA Given the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},A = {0, 2, 4, 5, 9}, andB = {1, 2, 7, 8, 9}use DeMorgan’s laws to find:•Find the set .•Find the set . BA BA A nonprofit organization’s board of directors, composed of four women (Angela, Betty, Carmine, and Delores) and three men (Ed, Frank, and Grant), holds frequent meetings.( A meeting can be held at Betty’s house, at Delores’s house, or at Frank’s house. •Delores cannot attend any meetings at Betty’s house•Carmine cannot attend any meetings on Tuesday or on Friday•Angela cannot attend any meetings at Delores’s house. •Ed can attend only those meetings that Grant also attends. •Frank can attend only those meetings that both Angela and Carmine attend.Restrictions •Delores cannot attend any meetings at Betty’s house•Carmine cannot attend any meetings on Tuesday or on Friday•Angela cannot attend any meetings at Delores’s house. •Ed can attend only those meetings that Grant also attends. •Frank can attend only those meetings that both Angela and Carmine attend. If the meeting is held on Tuesday at Betty’s, which of the following pairs can be among the board members who attend? 1.( Angela and Frank2.( Ed and Betty3.( Carmine and Ed4.( Frank and Delores5.( Carmine and AngelaCreator and ProducerElizabeth Jones forThe School of Mathematical and Statistical SciencesatArizona State University VideographerMike Jones©2009 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State
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