Slide 1Sets and Set OperationsObjectivesVocabularySet Vocabulary:Slide 6Determine if the given set is well defined.Slide 8Slide 9Given the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {0, 2, 4, 5, 6, 8}, and B = {1, 3, 5, 7} Answer the questions below:Slide 11Slide 12Slide 13Slide 14Slide 15CardsSlide 17Slide 18Slide 19Slide 20Creator 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 SeriesSets and Set OperationsObjectives•Determine if a set is well defined. •Write all the subsets of a given set and label the subsets as proper or improper. •Given a universal set and some subsets, find a complement, intersection or union. •Draw a Venn diagram to illustrate two sets. •Use the cardinal number formula.Vocabulary•roster notation •set-builder notation •well defined set •cardinal number •empty set •subset •proper/improper subset •intersection of sets •union of sets •mutually exclusive •complement of a setSet Vocabulary:roster notation:set builder notation:a complete or implied listing of all the elements of the set used when the roster method is cumbersome or impossibleSet Vocabulary:well defined set:A set is well-defined if any given object either is an element of the set, or is not an element of the setDetermine if the given set is well defined.The set of all good bandsThe set of odd numbersThe set of small numbers- well defined- not well defined- not well definedSymbols related to sets:Symbol Term or { }empty setinnot inn(A)numberSymbols related to sets:Term Symbol Read asunionorintersectionandcomplementnot (in A)subsetAGiven the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},A = {0, 2, 4, 5, 6, 8}, andB = {1, 3, 5, 7}Answer the questions below:•Find n(B).•Find the set A B.•Find the set n(B) = 4 = {0, 2, 4, 6, 8, 9}A B = {5}These are the things that are in set A and also in set B at the same time.These are the things that are in set U (the universe for our problem) that are not in set B.BBGiven the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},A = {0, 2, 4, 5, 6, 8}, andB = {1, 3, 5, 7}Answer the questions below:•Find the set .•Is 7A true or false?•Is 5B true or false?BA Cardinal Number Formula for the Union of Setsn(AB) = n(A) + n(B) — n(AB)FormulasCardinal Number Formula for the Complement of a Set)()()( AnAnUn If n(A B) = 40, find n(AB) and draw a Venn diagram to illustrate the composition of U.Suppose n(U) = 61, n(A) = 32, and n(B) = 26.n(AB) = n(A) + n(B) — n(AB)In a recent health survey, 750 single men in their twenties were asked to check the appropriate box or boxes on the following form.I am a member of a private gym.I am a vegetarian.The results were tabulated as follows: 374 checked the gym box92 checked the vegetarian box332 were blank (no boxes checked)750 men surveyed 374 checked the gym box92 checked the vegetarian box332 were blank (no boxes checked)1.Draw a Venn diagram illustrating the results of the survey.2.What percent of these men were both members of a private gym and vegetarians.CardsCardsDetermine how many cards, in an ordinary deck of 52, are clubs or twos.CardsDetermine how many cards, in an ordinary deck of 52, are face cards or diamonds.CardsDetermine how many cards, in an ordinary deck of 52, are threes or sixes.CardsDetermine how many cards, in an ordinary deck of 52, are threes and sixes.Creator 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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