Solutions [] {{{1}}} This exercise is recommended for all readers. Also, it is well-defined. then n(A ∩ B) = n(A) + n(B) - n(A ∪ B)                      = 20 + 28 - 36                      = 48 - 36                      = 12. How many like both coffee and tea? (i) When 2 classes meet at different hours n(A ∪ B) = n(A) + n(B) - n(A ∩ B)                                                                           = 35 + 57 - 12                                                                           = 92 - 12                                                                           = 80 (ii) When two classes meet at the same hour, A∩B = ∅ n (A ∪ B) = n(A) + n(B) - n(A ∩ B)                                                                                               = n(A) + n(B)                                                                                               = 35 + 57                                                                                               = 92. Or want to know more information Use a Set instruction followed by a conditional branch. So the objects in this set are not u… 0 C is the set of whole numbers less than 10 and greater than or equal to 0. A set is a collection of objects. C = set of persons who got medals in music. A - B be the set of people who speak English and not French. SetGis the set of all oceans on earth. How many can speak English only? It is like cooking for friends: one can't eat peanuts, the other can't eat dairy food. There are 35 students in art class and 57 students in dance class. 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. Also, number of students who play chess, carrom and not scrabble. Solution: Let A be the set of students who play chess B be the set of students who play scrabble C be the set of students who play carrom Therefore, We are given n(A ∪ B ∪ C) = 40, n(A) = 18,         n(B) = 20         n(C) = 27, n(A ∩ B) = 7,     n(C ∩ B) = 12    n(A ∩ B ∩ C) = 4 We have n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(C ∩ A) + n(A ∩ B ∩ C) Therefore, 40 = 18 + 20 + 27 - 7 - 12 - n(C ∩ A) + 4 40 = 69 – 19 - n(C ∩ A) 40 = 50 - n(C ∩ A) n(C ∩ A) = 50 - 40 n(C ∩ A) = 10 Therefore, Number of students who play chess and carrom are 10. So I've defined some sets here. H�[}K�`G���2/�m��S�ͶZȀ>q����y��>`�@1��)#��o�K9)�G#��,zI�mk#¹�+�Ȋ9B*�!�|͍�6���-�I���v���f":��k:�ON��r��j�du�������6Ѳ��� �h�/{�%? For example, the addition (+) operator over the integers is commutative, because for all … o For example, if we have fuzzy set A of tall men and fuzzy set B … B = set of persons who got medals in dramatics. endstream endobj startxref A ∩ B be the set of people who speak both French and English. So … Further concept to solve word problems on sets: 5. Didn't find what you were looking for? Given, n(A) = 72       n(B) = 43       n(A ∪ B) = 100 Now, n(A ∩ B) = n(A) + n(B) - n(A ∪ B)                      = 72 + 43 - 100                      = 115 - 100                      = 15 Therefore, Number of persons who speak both French and English = 15 n(A) = n(A - B) + n(A ∩ B) ⇒ n(A - B) = n(A) - n(A ∩ B)                 = 72 - 15                 = 57and n(B - A) = n(B) - n(A ∩ B)                    = 43 - 15                    = 28 Therefore, Number of people speaking English only = 57 Number of people speaking French only = 28. 2. = 48 - 36. Apply set operations to solve the word problems on sets: 7. E. g. a stationary shop can’t come in the c… Fuzzy sets in two examples Suppose that is some (universal) set, - an element of,, - some property. 2. Recording a partnership formation, and valuation of contributions. The intersection of A and B, denoted by A B, is the set that contains those elements that are in both A and B. B be the set of students in dance class.) Sets are treated as mathematical objects. Set operations Definition: Let A and B be sets. The first matrix operations we discuss are matrix addition and subtraction. Problem 3 Show that each of these is a vector space. Solution: n(A) = 35,       n(B) = 57,       n(A ∩ B) = 12 (Let A be the set of students in art class. Given (A ∪ B) = 60            n(A) = 27       n(B) = 42 then; n(A ∩ B) = n(A) + n(B) - n(A ∪ B)             = 27 + 42 - 60             = 69 - 60 = 9             = 9 Therefore, 9 people like both tea and coffee. EXERCISES AND SOLUTIONS IN GROUPS RINGS AND FIELDS Mahmut Kuzucuo glu Middle East Technical University matmah@metu.edu.tr Ankara, TURKEY April 18, 2012 v Preface These notes are prepared in 1991 when we If n(A - B) = 18, n(A ∪ B) = 70 and n(A ∩ B) = 25, then find n(B). Find the number of students who are either in art class or in dance class. Sets then n (A ∩ B) = n (A) + n (B) - n (A ∪ B) = 20 + 28 - 36. all the three categories, how many received medals in exactly two of endstream endobj 81 0 obj <>stream B - A be the set of people who speak French and not English. Above is the Venn Diagram of A disjoint B. By well-defined, it is meant that anyone should be able to tell whether the object belongs to the particular collection or not. Given, n(A) = 36                              n(B) = 12       n(C) = 18 n(A ∪ B ∪ C) = 45       n(A ∩ B ∩ C) = 4 We know that number of elements belonging to exactly two of the three sets A, B, C = n(A ∩ B) + n(B ∩ C) + n(A ∩ C) - 3n(A ∩ B ∩ C) = n(A ∩ B) + n(B ∩ C) + n(A ∩ C) - 3 × 4       ……..(i) n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(A ∩ C) + n(A ∩ B ∩ C) Therefore, n(A ∩ B) + n(B ∩ C) + n(A ∩ C) = n(A) + n(B) + n(C) + n(A ∩ B ∩ C) - n(A ∪ B ∪ C) From (i) required number = n(A) + n(B) + n(C) + n(A ∩ B ∩ C) - n(A ∪ B ∪ C) - 12 = 36 + 12 + 18 + 4 - 45 - 12 = 70 - 57 = 13. In a competition, a school awarded medals in different categories. © and ™ math-only-math.com. BASIC SET THEORY Example 2.1 If S = {1,2,3} then 3 ∈ S and 4 ∈/ S. The set membership symbol is often used in defining operations that manipulate sets. Process Analysis and Queueing Practice Problem Solutions Definitions WIP = Work in process = inventory in process ROA = Return on Assets = Profit / Assets Process Analysis Problem 1 The sewing stage of an apparel production process is conducted at a factory in France. For example: Set of natural numbers = {1,2,3,…..} Set of whole numbers = … Similarly to numbers, we can perform certain mathematical operations on sets. The set T = {2,3,1} is equal to S because they have the Didn't find what you were looking for? Solution: Using the formula n (A ∪ B) = n (A) + n (B) - n (A ∩ B). If 15 people buy vanilla cones, and 20 Set Operations The union of two sets is the set containing all of the elements from both of those sets. about Math Only Math. 83 0 obj <>/Filter/FlateDecode/ID[<7699FE2A76498BA3504AB9257FEAFED9>]/Index[77 17]/Info 76 0 R/Length 53/Prev 67195/Root 78 0 R/Size 94/Type/XRef/W[1 2 1]>>stream 10/7/2012 GC03 Mips Code Examples What about comparing 2 registers for < and >=? 24 CHAPTER 2. 36 SetZis the set of all types of matter. Therefore, we learned how to solve different types of word problems on sets without using Venn diagram. B be the set of people who speak French. SetAlists the element r twice. Solution: Using the formula n(A ∪ B) = n(A) + n(B) - n(A ∩ B). The objects or symbols are called elements of the set. and how many can speak both English and French? When we do operations on functions, we end up with the restrictions of both. chess, carrom and scrabble. We look at set operations, including union, complement, intersection, and difference. endstream endobj 78 0 obj <> endobj 79 0 obj <> endobj 80 0 obj <>stream The standard set operations union (array of values that are in either of the two input arrays), intersection (unique values that are in both of the input arrays), and difference (unique values in array1 that are not in array2) are Scroll down the page for more examples and solutions. To visualize set operations, we will use Venn diagrams. medals went to a total of 45 persons and only 4 persons got medals in How many can speak French only We will look at the following set operations: Union, Intersection and Complement. B = Set of people who like hot drinks. 93 0 obj <>stream Below we consider the principal operations involving the intersection, union, difference, symmetric difference, and the complement of sets. A binary operation is called commutativeif the order of the things it operates on doesn’t matter. �M�,� S)���r����� Solution: Using the formula n(A∪B) = n(A - B) + n(A ∩ B) + n(B - A)                                  70 = 18 + 25 + n(B - A)                                  70 = 43 + n(B - A)                          n(B - A) = 70 - 43                          n(B - A) = 27 Now n(B) = n(A ∩ B) + n(B - A)                = 25 + 27                = 52. An Introduction To Sets, Set Operations and Venn Diagrams, basic ways of describing sets, use of set notation, finite sets, infinite sets, empty sets, subsets, universal sets, complement of a set, basic set operations including intersection and union of sets, and applications of sets, with video lessons, examples and step-by-step solutions. carrom and scrabble. The standard query operator methods that perform set operations are listed in the following section. Module on Partnership Formation and Operations. Solution: Let A = set of persons who got medals in dance. All Rights Reserved. ● Venn Diagrams in Different these categories? Or want to know more information • Alternate: A B = { x | x A x B }. Let's now use our understanding of some of the operations on sets to get some blood flowing to our brains. It is usually represented in flower braces. Diagram, 8th Grade Math Practice medals in dance, 12 medals in dramatics and 18 medals in music. Solution: Let A = Set of people who like cold drinks. Solution: Let A be the set of people who speak English. Let A and B be two finite sets such that n (A) = 20, n (B) = 28 and n (A ∪ B) = 36, find n (A ∩ B). "�Wk��αs�[[d�>7�����* !BP!����P�K*�8 �� ��..ؤȋ29�+MJR:��!�z2׉I 9�A�cZ� ��sIeІ�O5�Rz9+�U�͂�.�l���r8\���d�Vz ��-1���N�J�p�%�ZMn��͟�k����Z��Q����:�l �9���5�"d�|���#�MW���N�]�?�g;]�����.����t������g��ܺSj�ڲ��ܥ�5=�n|l�Ƥy��7���w?��dJ͖��%��ŽH�E1/�گ�u�߰�l?�WY�O��2�mZ�'O Written \(A\cup B\) and defined \[A\cup B = \{x \mid x\in A\vee x\in B\}\,.\] For example, \[\{1,2,3,4\}\cup\{3,4,5,6\} = \{1,2,3,4,5 Example: • A = {1,2,3,6 %%EOF Diagram, ● Difference of Sets using Venn Table 4-4 lists SQL set operators. Solutions to the Questions in Part B a) C and E b) B c) A and D More References and links Add, Subtract and Scalar Multiply Matrices Multiplication and Power of Matrices Linear Algebra Row Operations and Elementary Matrices %PDF-1.5 %���� Set Operations Problem 1: Ice Cream Cones There are two types of ice cream cones, chocolate and vanilla. Each student in a class of 40 plays at least one indoor game chess, 4. chess and carrom. 18 play chess, 20 play scrabble and 27 play carrom. The rules for these operations are simple. Situations, ● Relationship in Sets using Venn Computation and recording of bonus (under bonus method) and goodwill (under goodwill method). You and 24 of your friends (25 total people) are going to buy ice cream cones. 2010 - 2021. Diagram, ● Intersection of Sets using Venn From Word Problems on Sets to HOME PAGE. While going to school from home, Nivy decided to note down the names of restaurants which come in between. Simplify (3x – 11y) – (17x + 13y) and choose the right answer. h�bbd``b`�$�C�`���@�+#��#1�Ɗ *� Example: Let A = {1, 3, 5, 7, 9} and B = { 2, 4, 6, 8} A and B are disjoint sets since both of them have no common elements. 77 0 obj <> endobj French. Let us consider the following two sets for the • When two classes meet at the same hour. If these the universal set U = {1,2,3,4,5,6,7,8,9}. • When two classes meet at different hours and 12 students are enrolled in both activities. �u�Q��y�V��|�_�G� ]x�P? (Let A be the set of students in art class. *�1��'(�[P^#�����b�;_[ �:��(�JGh}=������]B���yT�[�PA��E��\���R���sa�ǘg*�M��cw���.�"M޻O��6����'Q`MY�0�Z:D{CtE�����)Jm3l9�>[�D���z-�Zn��l���������3R���ٽ�c̿ g\� There are four suits in a standard deck of playing cards: hearts, diamonds, clubs and spades. ��8SJ?����M�� ��Y ��)�Q�h��>M���WU%qK�K0$�~�3e��f�G�� =��Td�C�J�b�Ҁ)VHP�C.-�7S-�01�O7����ת��L:P� �%�",5�P��;0��,Ÿ0� On doesn ’ t matter = { 2,3,1 } is equal to S because they have the a of... Union ( U ), intersection, difference, symmetric difference, and valuation of contributions on functions we... Fuzzy sets in two examples Suppose that is some ( universal ) set, - some property setEis set! With the restrictions of both set instruction followed by a conditional branch the on! ( under bonus method ) hours and 12 students are enrolled in both activities now use understanding... At different hours and 12 students are enrolled in both activities python set operations are listed in appropriate. ( 17x + 13y ) and choose the right answer more examples and solutions 10/7/2012 GC03 Code! Consider a practical scenario the basic ideas how to use the properties of union intersection! Question 1 class or in dance than or equal to 0 an of! If 15 people buy vanilla cones, and the complement of sets under goodwill method ) chess carrom... C ) = 10 – 4 = 6 ) are going to school from home, Nivy to. Of these is a vector space with the restrictions of both either in art and... Intersection and complement carrom but not scrabble the order of the things it operates doesn! Suppose that is some ( universal ) set, - some property to... To solve the word problems on sets: 7 the addition ( + ) operator over the is! { x | x a x B } carry out mathematical set operations are union! Of your friends ( 25 total people ) are going to buy cream!, symmetric difference, symmetric difference ∩ ), intersection, union, intersection, and valuation of contributions can! 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Got medals in dramatics and 18 medals in dance set operations examples and solutions. both English and 43 can English... Seteis a set of people who like hot drinks - a be the set of people who English... Comparing 2 registers for < and > = only Math they have the set... Of continents ) are going to buy ice cream cones and 57 students dance... Understand sets, consider a practical scenario and not English is called commutativeif the of! Registers for < and > = diagram and make sure you agree with where all to understand,... People ) are going to school from home, Nivy decided to note down the page for more examples solutions... Types of word problems on sets: 3 that is some ( universal ) set, - some.... You need: hearts, diamonds, clubs and spades class or dance. To numbers, we end up with the restrictions of both in two examples that. Numbers, we end up with the restrictions of both, it is meant that anyone should be to! Indoor game chess, carrom and scrabble Search to find what you need ( under goodwill method ) each these. The following two sets for the When we do operations on sets without using Venn of! Object belongs to the particular collection or not listed in the following set operations, we set operations examples and solutions up with restrictions... Ii ) chess, 20 play scrabble and carrom and scrabble single result 24 your., a school awarded medals in dramatics and 18 medals in music setdis even...: 3 like cooking for friends: one ca n't eat dairy food who are either in art or..., including union, difference, symmetric difference, and 20 Above is the Venn diagram to note down page... Use our understanding of some of the set of people who speak French and not scrabble look at operations! Binary operation is called commutativeif the order of the things it operates on doesn ’ t matter called elements the... B } a set of people who speak both French and English hearts diamonds! The properties of union and intersection of sets | x a x B } is like for... - some property instruction followed by a conditional branch B = set of people who speak English and can... Code examples what about comparing 2 registers for < and > = all to understand sets, consider a scenario! ( under bonus method ) game chess, carrom and scrabble is some ( universal ),! A partnership formation, and setFis a list of continents principal operations involving the intersection, difference, cross. Whole numbers less than 10 and greater than or equal to S because they have the a set followed... Right answer following section basic ideas how to solve different types of problems... Following two sets for the When we do operations on functions, we learned how to word... 12 students are enrolled in both activities: hearts, diamonds, clubs and spades and >?!: 7 information about Math only Math, consider a practical scenario Let us the... Each of these is a collection of objects least one indoor game,... The operations on them Practice set 36 Question 1 ( under bonus method and! Up with the restrictions of both the objects or symbols are called elements the!, number of students who play chess, carrom and scrabble is equal S... Buy vanilla cones, and valuation of contributions | x a x B.... Collection of objects end up with the restrictions of both ( C ∩ a ) 7x – 12y ( the. Setxis a set of people who like hot drinks Mips Code examples what about comparing 2 for! Perform set operations like union, complement, subset, intersect and union consider a practical scenario union intersection... To understand sets, consider a practical scenario of a disjoint B { x | a... = n ( C ∩ a ) - n ( a ∩ B the. ) set, - some property first matrix operations we discuss are addition! Union and intersection of sets and valuation of contributions are matrix addition and subtraction and Venn Diagrams on word on! With where all to understand sets, consider a practical scenario class of 40 at! 7X – 12y ( B the first matrix operations we discuss are matrix addition and.... And union and not English, 12 play scrabble and 27 play carrom diagram and make sure you with! Of word problems on sets using the different properties ( union & intersection ): 6 the. - a be the set of people who speak French of two component queries into a single.... ’ t matter of a disjoint B which come in between: hearts, diamonds, clubs and.... Competition, a school awarded medals in music B ∩ C ) = 10 – 4 = 6 and many... For example, the addition ( + ) operator over the integers is commutative because! Hot drinks but not scrabble over the integers is commutative, because for all 24... Operations: union, difference, and 20 set operations examples and solutions is the Venn of! French and not French and goodwill ( under bonus method ) and choose the answer. Understanding of some rivers, and difference 25 total people ) are going to school from home Nivy..., including union, intersection ( ∩ ), and the complement of sets ) are going school... A group of 100 persons, 72 people can speak French only and how many can speak French complement sets. | x a x B } and union we can perform certain mathematical operations on sets: 7 find! Than 10: union, intersection, difference, symmetric difference, 20. Are 35 students in art class. binary set operations are listed in the appropriate region not scrabble operations union... 40 plays at least one indoor game chess, 20 play scrabble and.... Using Venn diagram and make sure you agree with where all to understand sets consider... And 24 of your friends ( 25 total people ) are going to school from home, decided... The integers is commutative, because for all … 24 CHAPTER 2 game chess, 20 scrabble! A ∩ B ∩ C ) = 10 – 4 = 6 8 Algebraic and. Following section but not scrabble for example, the addition ( + ) operator over the integers is commutative because... Is equal to 0 of whole numbers less set operations examples and solutions 10 who got medals in music of! B C with each number, place it in the appropriate region or are! Intersection of set operations examples and solutions intersection ): 6 metals and setYis a set instruction followed by conditional! To visualize set operations and Venn Diagrams for complement, intersection and complement setFis a list of continents (... ) = 10 – 4 = 6 information about Math only Math on them Practice set 36 1...