Table of Contents. Sets

Transcription

1 Table of Contents SETS... 2 Problem 1: Create Venn Diagram - Coffee or Juice (Easy)... 3 Problem 2: Create Venn Diagram - NCIS or Good Wife (Easy)... 4 Problem 3: Create Venn Diagram - School Survey (Medium)... 5 Problem 4: Create Venn Diagram Survey (Easy)... 6 Problem 5: Create Venn Diagram - Students Courses (Medium)... 7 Problem 6: Create Venn Diagram - Human Blood Types (Medium)... 8 Problem 7: Create Venn Diagram - Blood Antigens (Medium) Answers Elementary Algebra Page 1

2 SETS A set is a defined list of elements. The following word problems require knowledge of Sets. Union of sets = all elements in one set or the other o A = {1,2} B = {0, 9}, A union B = {0, 1, 2, 9} Intersection of sets = All elements that are in all the sets o A = {1, 2, 3}, B = {9, 2, 1}, A intersection B = {1, 2} Difference of two sets (A B) = All elements of A that are not in B o A = {1, 2, 3}, B = {9, 2, 1}, A - B = {3} Venn diagram circles that represent relationships among sets. Figure 1. Venn Diagram Elementary Algebra Page 2

3 Problem 1: Create Venn Diagram - Coffee or Juice (Easy) At the teacher s faculty meeting, 40 teachers had coffee, 12 teachers had orange juice, and 10 teachers had coffee and orange juice. 5 teachers did not have anything to drink. a. How many teachers were at the meeting? Elementary Algebra Page 3

4 Problem 2: Create Venn Diagram - NCIS or Good Wife (Easy) In a class of 100 students, 45 watched NCIS, 34 watched Good Wife, and 10 watched both. Find the number of students that a. Didn t watch either show b. Watched NCIS only c. Watched Good Wife Only Elementary Algebra Page 4

5 Problem 3: Create Venn Diagram - School Survey (Medium) Southwestern High School performed a survey on subjects (mathematics, English, history) taken in The survey was taken by 300 students. The following data was revealed: 90 were taking mathematics 140 were taking history 60 were taking English 25 were taking mathematics and history 40 were taking history and English 10 were mathematics and English 5 were taking all the three subject a: How many students were not taken any subjects? Elementary Algebra Page 5

6 Problem 4: Create Venn Diagram Survey (Easy) Tenesia surveyed her 200 office workers to help her determine which soda machine to contract for the office. 100 of the workers preferred Pepsi, 75 preferred Coke, and 20 preferred both equally. a. How many preferred Pepsi Only? b. How many preferred Coke Only? c. How many did not prefer either one? Elementary Algebra Page 6

7 Problem 5: Create Venn Diagram - Students Courses (Medium) Karl asked 100 adults whether they had studied Calculus, Algebra, or Geometry in high school. 10 adults studied all three, 13 studied Calculus and Algebra, 15 studied Algebra and Geometry, 12 studied Calculus and Geometry, 20 studied Calculus, 20 studied Algebra, and 20 studied Geometry. a. How many studied Calculus only? b. How many studied Geometry Only? c. How many studied Algebra only? d. How many did not study any of the three? Elementary Algebra Page 7

8 Problem 6: Create Venn Diagram - Human Blood Types (Medium) Human blood types. There are 3 antigens that could be found in the blood (A sugar, B sugar, RH protein) and their absence or presence determines blood type. The Venn diagram (figure 1) has eight regions, one for each blood type. The diagram can be used to determine all compatible blood types for each of the eight blood types. The presence of the RH protein determines whether the type is + or -. Blood types are A+, A-, AB-, AB+, AB-, B+, B-, O+, and O-. The compatible blood types for B + are: B +, B -, O +, and O - because no new elements are introduced into the bloodstream. You should fill in the other seven diagrams showing compatible blood types for A+, A-, B-, AB+, AB -, O+, and O-. Elementary Algebra Page 8

9 O- A A- AB- B- B- B AB+ B+ A+ O+ RH a. Fill in the table below: Blood Type Compatible with... O + O - A + A - B + B +, B -, O +, O - B - AB + AB - Elementary Algebra Page 9

10 Problem 7: Create Venn Diagram - Blood Antigens (Medium) At Holy Cross hospital, the blood of 600 patients was tested. It was found that 328 patients had the A antigen, 60 had the B antigen and 422 had the RH antigen, while 35 had none of these. In addition, it was found that 18 had the A and B antigens, 51 had the B and RH antigens, 193 had the A and RH antigens and 13 had all three. How many a. Had none of the antigens? Elementary Algebra Page 10

11 Answers 1a: 47 2a: 31 2b: 35 2c: 24 3a: 85 4a: 80 4b: 55 4c: 45 5a: 5 5b: 3 5c: 2 5d: 70 6a: Blood Type Compatible with... O + O-, O+ O - O- A + A+, A-, O+, O- A - A-, O- B + B +, B -, O +, O - B - B-, O- AB + AB+, A+, B+,O+,AB-,A-, B-, O- AB - AB-, O-, A-,B- 7a: 31 Elementary Algebra Page 11