Math 7 Q1L3 Basic Set Operations PDF

7th Grade Quarter 1 Lesson 3: BASIC SET OPERATIONS Prepared by: Mr. Ace B. Contreras Mrs. Avelina T. Tuvera Ms. Chelsea Hilary B. Famarin  Learning Target 01 02 03 I can define I can perform I can solve real- Venn Di...

7th Grade Quarter 1 Lesson 3: BASIC SET OPERATIONS Prepared by: Mr. Ace B. Contreras Mrs. Avelina T. Tuvera Ms. Chelsea Hilary B. Famarin  Learning Target 01 02 03 I can define I can perform I can solve real- Venn Diagram. basic set life problems operations. involving set operations.  WHAT IS A VENN DIAGRAM?  VENN DIAGRAM Venn Diagrams are very useful in showing relationship between sets. It consists of a rectangle represents the universal set and a circle/s inside the rectangle to represent set/s being considered in the discussion. U A  VENN DIAGRAM FOR SET RELATIONS U A a e e∈A a∉A U A B A=B U A C B B⊆A A⊇B C⊄A  Disjoint Sets they don’t have any element in common. U O E 𝟏, 𝟑, 𝟓, 𝟕, … 𝟐, 𝟒, 𝟔, 𝟖, … 𝐎 = 𝟏, 𝟑, 𝟓, 𝟕, … 𝑬 = 𝟐, 𝟒, 𝟔, 𝟖, …  Joint Sets they have some elements in common. U A B 𝐛, 𝐜, 𝐝 𝐚, 𝐞 𝐢, 𝐨, 𝐮 𝐁 = 𝐚, 𝐞, 𝐢, 𝐨, 𝐮 𝐀 = {𝐚, 𝐛, 𝐜, 𝐝, 𝐞}  BASIC SET OPERATIONS  BASIC SET OPERATIONS As we all know, we have operations such as addition, subtraction, multiplication and division. In sets, we have union, intersection, complement and difference. Union of Sets the union of two sets A & B is a set that contains all the elements in a A and B. It is represented by the symbol “U”, denoted as A U B, and read as “A union B” Union of Sets U A B AUB  Examples: 1. Given: 𝐀 = 𝒂, 𝒆, 𝒊, 𝒐, 𝒖 and 𝑩 = 𝒂, 𝒃, 𝒄, 𝒅, 𝒆,. Find A U B. 2. U A B h r x o e c n t s u u 3. Given: 𝐗 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔}, 𝒀 = {𝟐, 𝟒, 𝟓, 𝟔} and 𝒁 = 𝟏, 𝟔, 𝟕. Find X U Y U Z. Intersection of Sets the intersection of two sets A & B is a set contains the elements in common to both A & B. It is represented by the symbol “Ո”, denoted as A Ո B and read as “A intersection B” Intersection of Sets U A B AՈB  Examples: 1. Given: 𝐀 = {𝟏𝟎, 𝟐𝟎, 𝟑𝟎, 𝟒𝟎, 𝟓𝟎} and 𝑩 = {𝟏𝟎, 𝟒𝟎, 𝟕𝟎, 𝟏𝟎𝟎, 𝟏𝟑𝟎}. Find A Ո B. 2. Given: 𝐀 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔}, 𝑩 = {𝟐, 𝟒, 𝟔} and 𝑪 = {𝟏, 𝟑, 𝟓, … } Find A Ո C. 3. Given: 𝐗 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔}, 𝒀 = {𝟐, 𝟒, 𝟓, 𝟔} and 𝒁 = 𝟏, 𝟔, 𝟕. Find X Ո Y Ո Z. Complement of Sets written as A’ or A is the set of all elements in the universal set (U) that are not in set A. Complement of Sets U A B A’ Complement of Sets U A B B’  Examples: 1. Given: 𝑼 = {𝒂, 𝒃, 𝒄, 𝒅, 𝒆}, 𝒀 = {𝒂, 𝒃}. Find Y’ Difference of Sets is a set of elements which belongs to A but which does not belong to B. It is written as A – B. Difference of Sets U A B A–B Difference of Sets U A B B–A  Examples: 1. Given: 𝐗 = {𝒂, 𝒃, 𝒄, 𝒅}, 𝒀 = {𝒄, 𝒅, 𝒆, 𝒇}. Find X – Y and Y – X. More Examples: More Examples: 1. Find: a. Universal Set b. A U B c. A Ո B d. A’ e. B’ f. A – B g. B – A More Examples: More Examples: 2. Find: a. Universal Set b. A U B c. A Ո B d. A’ e. B’ f. A – B g. B – A More Examples: More Examples: 3. Find: a. Universal Set b. A U B c. B U C d. A Ո B e. A Ո C f. A’ g. B’ More Examples: 3. Find: h. A – B i. B – A j. A – C k. A Ո (B U C) l. A U (B Ո C) m. (A U B)’ n. (A Ո C)’ More Examples: 3. Find: o. (A – B)’ p. (B – A)’ q. (A – C)’ r. (A U B) – C s. A U B U C t. (A U B U C)’ u. (B Ո C) - A  More Examples: 4. Use Venn Diagram to represent the given example: U = 𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔 𝐀 = 𝟐, 𝟒, 𝟔 𝐁 = 𝟏, 𝟐, 𝟑, 𝟔 REAL-LIFE EXAMPLES  Real-Life Examples: 1. Sarah has gumamelas and roses in her garden. Her gumamelas bear flower every September to December, and her roses from October to March. Let G be the set of months when the gumamelas bear flower and R be the set of months when the roses bear flower.  Real-Life Examples: 2. Find: a. Universal Set b. Elements of G and R c. G Ո R d. G U R e. (G U R)’  Real-Life Examples: 3. Ace and Yano must choose 2 ice cream flavors listed on the menu for their order. Ace chooses chocolate and vanilla. Yano chooses vanilla and cheese. Let A be the set of flavors chosen by Ace and Y be the set of flavors chosen by Yano. (Ice Cream Flavors: Chocolate, Vanilla, Cheese, Ube, Pandan, and Strawberry)  Real-Life Examples: 2.  Real-Life Examples: 2. Find: a. Flavors chosen by both. b. Ace and Yano but not both. c. No. of flavors chosen by Ace but not Yano. d. No. of flavors chose by neither Ace and Yano. COUNTING PROBLEMS  COUNTING PROBLEMS Counting problems occur in many areas of applied mathematics. To solve these counting problems, we often use Venn Diagram with concepts of union, intersection and complement of sets.  COUNTING PROBLEMS For example, if the following information are given: n(A Ո B Ո C) = 7 n(A Ո B ) = 10 n(B Ո C) = 11 n(A Ո C) = 7 n(A) = 22 n(B) = 18 n(C) = 17 n(U) = 41  Examples: 1. Out of 50 students, 20 are members of Math Club and 34 are members of Glee Club. If 8 are in both clubs, how many students are in: a. neither of the clubs? b. either of the clubs? c. Math Club but not in Glee Club? d. Glee but not Math Club?  Examples: 2. In a batch of 250 students, 62 are members of Sports Club, 170 students are members of Drama Club, and 40 students are in both clubs. How many students are in: a. either of the clubs? b. neither of the clubs? c. Drama Club but not in Sports Club? d. Sports Club but not Drama Club?  Examples: 3. A class adviser surveys 35 of his students on the kind of pets they have at home. He found that 15 have dogs, 12 have cats and 8 have birds. Five have dogs and cats, 4 have dogs and birds, and 2 have cats and birds. If no one has all three kind of pets, how many students have: a. none of these pets? b. cats but not dogs and birds? c. dogs and cats but not birds? d. birds but not cat and dogs? e. birds and cats but not dogs?  Examples: 4. A group of 100 students were surveyed, and it was found that each of the students surveyed liked at least one of the following three fruits: apples, bananas, and mangoes. 34 liked apples, 30 liked bananas, 33 liked mangoes, 11 liked apple and bananas, 15 liked bananas and mangoes, 17 liked apples and mangoes, 8 liked both three of the fruits. How many students: a. did not like any of the fruits? b. liked bananas and mangoes but not apples? c. liked apples but not banana and mangoes? d. liked bananas but not apples and mangoes?  Examples: 5. 50 nurses working for a particular nursing agency were asked if they had worked in private or public hospitals in the past two years. There were 11 who said they had worked in neither, while 17 said they had worked in both. If 27 had worked in private hospitals, how many nurses had worked in private but not in public hospitals? How many had worked in public but not in private hospitals?  Examples: 6. A Science teacher conducted a survey in her class. She found out that 19 students have a brother, 15 students have a sister, 7 students have both a brother and a sister, and 6 students do not have any siblings at all. How many students are there in her class? SEATWORK # Answer Exercise on your Skill Book in Mathematics 7.  Thanks! Do you have any questions? [email protected] CREDITS: This presentation template was created by Slidesgo, and includes icons by Flaticon and infographics & images by Freepik Please keep this slide for attribution