cKathryn Bollinger, October 4, 2011 1Week-In-Review #5 (6.1, 6.2, 6.3)1. A and B are sets of a universal set, U. Use set-builder notation to define:(a) AC(b) A ∩ B(c) A ∪ B(d) AC∩ BC2. U = the set of all TV watchersS = the set of people who watch soap operas on TVG = the set of people who watch game shows on TVP = the set of people who watch sports on TV(a) Describe each of the following sets in words. (Do not use math jargon!)(i) SC(ii) S ∩ PC(iii) S ∪ G ∪ P(iv) G ∩ (S ∪ P )(b) Write each of the following usin g set notation (ie: using only S, G, P, ∩ , ∪, and/orC)(i) The set of TV watchers who watch soap operas or game shows.(ii) The set of TV watchers who watch game shows, but not sports.(iii) Th e set of TV watchers who only watch sports.(iv) The set of TV watchers who watch soap operas or game shows, but n ot both.cKathryn Bollinger, October 4, 2011 23. U = {1,2,3,4,5,6,7,8,9,10}A = {x | x ∈ U and x is even}B = {x | x ∈ U and x is odd}C = {2,3,5,6,8,9}D = {1,7,10}(a) Draw a Venn diagram representing the sets.(b) Find the following sets:(i) AC(ii) D ∩ AC(iii) B ∩ CC(iv) (A ∪ B) ∩ CC(v) A ∪ (B ∩ CC)(c) Are the following true or false?(i) D ⊆ B(ii) ∅ ⊆ A(iii) {2, 4} ∈ A(iv) {3, 5, 9} ⊂ C(v) AC= B(vi) A ∪ AC= U(vii) B ∩ BC= 0(viii) ∅ ∈ A(ix) A ∪ B = U(x) 3 ∈ B(d) How many subsets and proper su bsets does each set (A, B, C, D, and U) have?cKathryn Bollinger, October 4, 2011 34. Shade the portion of the Venn diagram that represents the given s ets.(a) AC∩ B ∩ CC(b) AC∩ (B ∪ CC)ABCUABCU(c) (A ∪ B) ∩ CC(d) (A ∩ B) ∪ CCABCUABCU5. Of 100 people surveyed 50 people liked th e color blue, 60 liked the color yellow, and 70 likedblue or yellow. How many of the people surveyed liked(a) Both blue and yellow?(b) Either blue or yellow, but not both?(c) Neither blue nor yellow?(d) Only blue?(e) Only yellow?cKathryn Bollinger, October 4, 2011 46. A survey of 500 A&M students was taken to determine the readership of the Battalion, theBryan-College Station Eagle, and the Houston Chronicle. The s urvey found that• 424 read the Battalion• 34 read the Chronicle• 35 read the Eagle• 12 read the Battalion and Ch ronicle• 15 read the Battalion and Eagle• 9 read th e Chronicle and Eagle• 3 read all three papersHow many of the students surveyed(a) read none of the three papers?(b) read just the Eagle?(c) read the Battalion and the Chronicle, but not the Eagle?(d) read at least two of the three papers?cKathryn Bollinger, October 4, 2011 57. A survey of 500 A&M students was taken to determine the readership of the Battalion, theBryan-College Station Eagle, and the Houston Chronicle. The s urvey found that• 415 did not r ead the Chronicle, but did read either the Battalion or the Eagle• 402 read the Battalion but not the E agle• 25 read the Eagle, bu t not the Chronicle• 17 read the Battalion and the Chronicle• 14 read the Battalion and the Eagle• 9 read th e Chronicle and the Eagle• 10 read only the ChronicleHow many of the students(a) read all three of the papers?(b) read just the Battalion?(c) read either the Battalion or the Chronicle, but not both?(d) read at most one paper?cKathryn Bollinger, October 4, 2011 68. A breakfast special includes an entree, one side, and a choice of drink. There are 5 differententrees, 10 different sid es and 6 different drinks to choose from. How many different breakfastspecials are possible?9. How many different 4-digit codes are possible if(a) there are no restrictions placed on the digits?(b) no repetition of the digits is allowed?(c) every digit in the code must be odd?(d) the first digit must be even and no digit can be repeated?(e) the code must form an even number?(f) the code must have at least one digit that is different than the rest?cKathryn Bollinger, October 4, 2011 710. A group of 3 couples (Allison and David, Breanna and Ethan, and C assie and Frank) go to themovies and all sit in one row of 6 seats. In how many different ways can they be seated if(a) there are no seating restrictions?(b) the girls and boys are seated alternately?(c) Allison must sit on the left end seat and Frank must sit on the right end seat?(d) girls must be seated in th e m iddle two seats and boys must be seated in the end seats?(e) the couples must be seated next to one
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