Module week 2 Q1
- 2. MODULE 1
- 3. What is a set? A group or collection of objects a set is a well-defined collection of distinct objects, considered as an object in its own right.
- 4. Each objects in a set is called a MEMBER or an ELEMENT of a set. 𝜀
- 5. (ellipsis)
- 6. Given: U = {1, 2, 3, 4, 5, 6, 7, 8 , 9, 10, 11, 12, 13, 14} A={1, 2, 3, 4, 5, 6} B = {2, 4, 6, 8,10, 12, 14} C = {2, 3, 5, 7, 9, 11, 13} Draw a Venn diagram showing the relationships among the given sets.
- 8. Given: U = {1, 2, 3, 4, 5, 6, 7, 8 , 9, 10, 11, 12, 13, 14} A={1, 2, 3, 4, 5, 6} B = {2, 4, 6, 8,10, 12, 14} C = {2, 3, 5, 7, 9, 11, 13} Find: A’ ∪ B A’ = {7, 8 , 9, 10, 11, 12, 13, 14} A’ ∪ B = {2, 4, 6, 7, 8 , 9, 10, 11, 12, 13, 14} B = {2, 4, 6, 8,10, 12, 14}
- 9. Given: U = {1, 2, 3, 4, 5, 6, 7, 8 , 9, 10, 11, 12, 13, 14} A={1, 2, 3, 4, 5, 6} B = {2, 4, 6, 8,10, 12, 14} C = {2, 3, 5, 7, 9, 11, 13} Find: A ∩ U A ∩ U = {1, 2, 3, 4, 5, 6}
- 10. Given: U = {1, 2, 3, 4, 5, 6, 7, 8 , 9, 10, 11, 12, 13, 14} A={1, 2, 3, 4, 5, 6} B = {2, 4, 6, 8,10, 12, 14} C = {2, 3, 5, 7, 9, 11, 13} Find: A – B A – B = {1, 3, 5}
- 11. Given: U = {1, 2, 3, 4, 5, 6, 7, 8 , 9, 10, 11, 12, 13, 14} A={1, 2, 3, 4, 5, 6} B = {2, 4, 6, 8,10, 12, 14} C = {2, 3, 5, 7, 9, 11, 13} Find: B’ B’ = {1, 3, 5, 7, 9, 11, 13}
- 12. Given: U = {1, 2, 3, 4, 5, 6, 7, 8 , 9, 10, 11, 12, 13, 14} A={1, 2, 3, 4, 5, 6} B = {2, 4, 6, 8,10, 12, 14} C = {2, 3, 5, 7, 9, 11, 13} Find: B’ – C B’ = {1, 3, 5, 7, 9, 11, 13} B’ – C = {1} C = {2, 3, 5, 7, 9, 11, 13}
- 13. MODULE 2
- 14. Venn Diagrams
- 15. • use Venn diagrams to illustrate sets, subsets and set operations. • solve word problems involving sets with the use of Venn diagrams • apply set operations to solve a variety of word problems.
- 16. Venn Diagram is a diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by the areas of overlap among the circles.
- 17. John Venn
- 21. More Examples on Venn Diagram
- 22. 𝐴 = 𝑝, 𝑛, 𝑜, 𝑦 Elements which belong to set A
- 23. Elements which belong to set B 𝐵 = 𝑝, 𝑜, 𝑡
- 24. 𝐴 ∩ 𝐵 𝐴 𝑎𝑛𝑑 𝐵 𝐴 intersection 𝐵 Elements are common to set A and set B 𝐴 ∩ 𝐵
- 25. 𝐴 ∪ 𝐵 𝐴 𝑜𝑟 𝐵 𝐴 union 𝐵 Elements which belong to set A, or set B or to both sets 𝐴 ∪ 𝐵
- 26. A′ Complement of A Elements of U that do not belong to A
- 27. 𝐵′ Complement of B Elements of U that do not belong to B
- 28. 𝐴 − 𝐵 Difference of A and B Elements which belong to set A but which do not belong to set B
- 31. Another example…
- 32. A class of 25 students were surveyed and asked if they have a brother or a sister. Eight students said they have only a brother, 6 students said they have only a sister, another six said they have both a brother and a sister and 5 said they don’t have a brother or a sister.
- 33. Set-up of the Venn diagram based on the given problem
- 34. There are problems which involve 3 sets. The shaded parts of the sets are named and identified.
- 40. Let’s apply….
- 41. A group of students were interviewed on what colors they like. Below are their responses.
- 42. How many students like blue color? How many students like yellow and red? How many students like yellow or blue? How many students like yellow only? How many students like yellow, blue and red? How many students like blue or red but not yellow? How many students like neither yellow, blue nor red? 25 8 39 5 30 2 11
- 43. More example…
- 44. The Venn diagram displays the results of a survey to 100 students in Muntinlupa Science High School of whom owns a pet at home.
- 45. How many students owned only a dog? 51 How many students owned only a cat? 17 How many students owned only a bird? 7 How many students owned a dog but not a cat? 56 How many students owned a cat? 35 How many students owned a cat and a bird? 9 How many students owned a dog and a bird but not a cat? 5 How many students owned a dog or a cat but not a bird? 77 How many students owned none of the three pets? 2 How many students own all of the three pets? 6
- 46. More example…
- 47. In a survey, seventy-five students were interviewed on which subject they like better, English or Mathematics? Here is the result. 45 students like English 32 students like Mathematics 12 students like both Mathematics and English How many students like Mathematics only? How many students like English only? How many students dislike the two subjects?
- 48. English Math 201233 10 U 45 students like English 32 students like Mathematics 12 students like both Mathematics and English 32 - 1245 - 1275 - 65 75 students
- 49. In a survey, seventy-five students were interviewed on which subject they like better, English or Mathematics? Here is the result. 45 students like English 32 students like Mathematics 12 students like both Mathematics and English How many students like Mathematics only? How many students like English only? How many students dislike the two subjects? 20 33 10
- 50. Another example…
- 51. Among the 50 pupils of Muntinlupa Elementary School, 32 likes gumamela flower while 26 likes rose flower. How many pupils like gumamela flower and rose flower? How many pupils like gumamela flower only?
- 52. GumamelaRose U 818 24 32 likes gumamela flower 26 likes rose flower 50 pupils of Muntinlupa Elementary School
- 53. Among the 50 pupils of Muntinlupa Elementary School, 32 likes gumamela flower while 26 likes rose flower. How many pupils like gumamela flower and rose flower? How many pupils like gumamela flower only? 8 24
- 54. Another example…
- 55. Out of fifty students, 23 joined Mathematics club and 32 joined English club. If 8 joined in both Mathematics and English club, How many have joined the English club only? How about in Mathematics club only? How many are neither in Mathematics nor in English club?
- 56. 8 joined in both Mathematics and English club 32 joined English club 23 joined Mathematics club Out of 50 students
- 57. 8 8 joined in both Mathematics and English club 32 joined English club 23 joined Mathematics club English Math 23 – 8 1524 32 – 8 U Out of 50 students 50 – 47 3
- 58. Out of fifty students, 23 joined Mathematics club and 32 joined English club. If 8 joined in both Mathematics and English club, How many have joined the English club only? How about in Mathematics club only? How many are neither in Mathematics nor in English club? 24 15 3
- 59. Another example…
- 61. A group of 50 students went to a tour in Palawan province. Out of the 50 students, 24 joined the trip to Coron, 18 went to Tubbataha Reef, 20 visited El Nido, 12 made a trip to Coron and Tubbataha Reef, 15 saw Tubbataha Reef and El Nido, 11 made a trip to Coron and El Nido and 10 saw the three tourist spots. Questions: a. How many students went to Coron only? b. How many students went to Tubbataha Reef only? c. How many joined the El Nido trip only? d. How many did not go to any of the tourist spots?
- 62. 50 students went in a tour in Palawan province. 24 joined the trip to Coron,(C) 18 went to Tubbataha Reef, (T) 20 visited El Nido, (E) 12 made a trip to Coron and Tubbataha Reef, 15 saw Tubbataha Reef and El Nido, 11 made a trip to Coron and El Nido 10 saw the three tourist spots.
- 63. 10 CoronU Tubbataha El Nido 1 5 2 4 1 11 16 10 saw the three tourist spots 50 students went in a tour in Palawan province. 24 joined the trip to Coron 18 went to Tubbataha Reef 20 visited El Nido 12 made a trip to Coron and Tubbataha Reef 15 saw Tubbataha Reef and El Nido 11 made a trip to Coron and El Nido
- 64. “side to side”
- 65. Among the 50 pupils of Muntinlupa Elementary School, 32 likes gumamela flower while 26 likes rose flower. How many pupils like gumamela flower and rose flower? How many pupils like gumamela flower only?
- 66. GumamelaRose U x26 – x 32 – x 32 likes gumamela flower 26 likes rose flower 50 pupils of Muntinlupa Elementary School
- 67. 26 – x + x 32 – x+ = 50
- 69. Another example…
- 70. Among the 40 students of section Arrhenius, 23 loves singing and 25 loves dancing. How many students love singing and dancing? How many students love singing only?
- 71. Dance Sing 25 loves dancing 23 loves singing x25 – x 23 – x U 40 students of section Arrhenius
- 72. x25 – x 23 – x+ + = 40
- 73. Dance Sing 8 25 loves dancing 23 loves singing 17 15 U
- 74. Among the 40 students of section Arrhenius, 23 loves singing and 25 loves dancing. How many students love singing and dancing? How many students love singing only? 8 15
- 76. 113 Munscian students were surveyed and it was found out that all of them have visited at least one of the following three provinces: Abra, Bataan, and Cavite. 66 of the students visited Abra. 52 of the students visited Bataan. 76 of the students visited Cavite 19 of the students visited Abra and Bataan. 28 of the students visited Bataan and Cavite. 42 of the students visited Abra and Cavite. 40 of the students visited exactly one of the following three cities: Abra, Bataan, and Cavite. a. How many students visited only Abra? b. How many students visited only Bataan? c. How many students visited only Cavite? d. How many students visited both Abra and Bataan, but not Cavite? e. How many students visited both Bataan and Cavite, but not Abra? f. How many students visited both Abra and Cavite, but not Bataan? g. How many students visited all of the following three cities: Abra, Bataan, and Cavite?
- 77. In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least one of the two drinks. How many like both hot and cold drinks? 3 of the students in Sir G's class have been to Archimedes. 4 students have been to Ampere, and 1 student has been to both Archimedes and Ampere. How many students have been to Archimedes but not Ampere?