# equivalence class questions

Email. Modulo Challenge. 19, 24 and 21 falls under valid class. Equivalence partitions are also known as equivalence classes – … Here R is known as _____ a) equivalence relation b) reflexive relation c) symmetric relation d) transitive relation Within * each equivalence class, the items are returned randomly * (by shuffling the elements in the equivalence class every time * that equivalence class is reached during iteration). What is the value of 1 ∪ 2 ∪ 3 and 1 ∩ 2 ∩ 3 Let R = {(1, 1), (2, 2), (3, 3)} be an equivalence relation A1 is the equivalence class containing one element as 1 ∴ A1 = {1} A2 is the equivalence class containing one element as 2 ∴ A2 = {2} A3 is the equivalence class containing one element as 3 ∴ A3 = {3} Now, 1 ∪ 2 … 1. Let R be the equivalence relation on A × A defined by (a, b)R(c, d) iff a + d = b + c . In equivalence partitioning, inputs to the software or system are divided into groups that are expected to exhibit similar behavior, so they are likely to be proposed in the same way. What are [5] + [8] & [5] x [8]? Collecting everything that is equivalent to gives us and similarly for , we get . Find the equivalence class [(1, 3)]. 17 fall under an invalid class. So this class becomes our valid class. Now your probably thinking that modular arithmetic is kinda useless because you keep getting the same answers over and over again. Discrete Math. Lecture 7: Equivalence classes. University Math Help. a) equivalence relation my video related to the mathematical study which help to solve your problems easy. 17, 00:07: Es geht um einen Bericht über einen Brandfall (Verkleidung Cheminée). If I choose one of the equivalence classes and give a DFA for the class, then the DFA is a "subDFA" of M, with states from the class. We now look at how equivalence relation on partitions the original set . The classes will be as follows: © 2011-2020 Sanfoundry. Consider the equivalence relation on given by if . 2. A black box testing technique than can only be used during system testing, c. A black box testing technique appropriate to all levels of testing, d. A white box testing technique appropriate for component testing, a. So the answer is ‘A’ Question #2) a. d) {5, 25, 125,…} c) An input or output range of values such that each value in the range becomes a test case. View Answer, 9. of all elements of which are equivalent to . You’re right! To practice all areas of Discrete Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers. View Answer, 3. c) 16 All Rights Reserved. equivalence class [MATH.] Question 1: Let assume that F is a relation on the set R real numbers defined by xFy if and only if x-y is an integer. Now we have that the equivalence relation is the one that comes from exercise 16. here is complete set of 1000+ Multiple Choice Questions and Answers, Prev - Discrete Mathematics Questions and Answers – Relations – Partial Orderings, Next - Discrete Mathematics Questions and Answers – Graphs – Diagraph, Discrete Mathematics Questions and Answers – Relations – Partial Orderings, Discrete Mathematics Questions and Answers – Graphs – Diagraph, C++ Programming Examples on Graph Problems & Algorithms, C Algorithms, Problems & Programming Examples, Engineering Mathematics Questions and Answers, Training Classes on C, Linux & SAN – Group Photos, Java Programming Examples on Utility Classes, Discrete Mathematics Questions and Answers – Logics – Logical Equivalences, Discrete Mathematics Questions and Answers – Discrete Probability – Mean and Variance of Random Variables, Discrete Mathematics Questions and Answers – Groups – Closure and Associativity, Discrete Mathematics Questions and Answers – Types of Matrices, Discrete Mathematics Questions and Answers – Properties of Matrices, Discrete Mathematics Questions and Answers – Operations on Matrices, Discrete Mathematics Questions and Answers – Discrete Probability – Generating Functions, Discrete Mathematics Questions and Answers, Discrete Mathematics Questions and Answers – Discrete Probability – Power Series, Discrete Mathematics Questions and Answers – Groups – Cosets, Discrete Mathematics Questions and Answers – Discrete Probability – Logarithmic Series, Disjoint-Set Data Structure Multiple Choice Questions and Answers (MCQs), Discrete Mathematics Questions and Answers – Advanced Counting Techniques – Recurrence Relation. a) 125 The next £1500 is taxed at 10%. Equivalence Classes . equivalence relation and the equivalence classes of R are the sets of F. Pf: Since F is a partition, for each x in S there is one (and only one) set of F which contains x. Practice: Modular addition. MY VIDEO RELATED TO THE MATHEMATICAL STUDY WHICH HELP TO SOLVE YOUR PROBLEMS EASY. Transcript. Then , , etc. ... without demonstration of equivalence: Letzter Beitrag: 30 Mär. Equivalence Partitioning also called as equivalence class partitioning. It is a software testing technique that divides the input test data of the application under test into each partition at least once of equivalent data from which test cases can be derived. The equivalence classes that are divided perform the same operation and produce same characteristics or behavior of the inputs provided. And the equivalence . An employee has £4000 of salary tax free. The leftmost two triangles are congruent, while the third and fourth triangles are not congruent to any other triangle shown here. View Answer, 10. b) {2, 4, 9, 11, 15,…} Less than 1, 1 through 15, more than 15, b. Which of the following relations is the reflexive relation over the set {1, 2, 3, 4}? Sanfoundry Global Education & Learning Series – Discrete Mathematics. a) 23585 this video specially related to the topic equivalence classes. All the data items lying in an equivalence class are assumed to be processed in the same way by the software application to be tested when passed as input. webdhoom.com. and it's easy to see that all other equivalence classes will be circles centered at the origin. Which of these groups of numbers would fall into the same equivalence class? b) 5 a) 17 b) 19 c) 24 d) 21. a) {−21, −18, −11, −4, 3, 10, 16} c) {−24, -19, -15, 5, 0, 6, 10} b) 2.02 * 1087 Identify the invalid Equivalence class. c) An input or output range of values such that each value in the range becomes a … c) symmetric relation a) Less than 1, 1 through 12, larger than 12, b) Less than 1, 1 through 11, larger than 12, c) Less than 0, 1 through 12, larger than 12. Let us take the set . Therefore xFx. Practice: Modulo operator. Prove that F is an equivalence relation on R. Solution: Reflexive: Consider x belongs to R,then x – x = 0 which is an integer. Suppose a relation R = {(3, 3), (5, 5), (5, 3), (5, 5), (6, 6)} on S = {3, 5, 6}. Question 1 Let A ={1, 2, 3, 4}. Hier geht es insbesond… 5 Antworten: mechanism for a decision on recognition of equivalence: Letzter Beitrag: 08 Okt. Transcript. An equivalence class is defined as a subset of the form {x in X:xRa}, where a is an element of X and the notation "xRy" is used to mean that there is an equivalence relation between x and y. b) {…, -3, 0, 6, 21, …} View Answer, 4. were given an equivalence relation and were asked to find the equivalence class of the or compare one to with respect to this equivalents relation. Determine the number of equivalence classes that can be described by the set {2, 4, 5}. The technique is to divide (i.e. Now we have that the equivalence relation is the one that comes from exercise 16. Equivalence Partitioning is also known as Equivalence Class Partitioning. of all elements of which are equivalent to . The above are not handled by BVA technique as we can see massive redundancy in the tables of test cases. We can draw a binary relation A on R as a graph, with a vertex for each element of A and an arrow for each pair in R. For example, the following diagram represents the relation {(a,b),(b,e),(b,f),(c,d),(g,h),(h,g),(g,g)}: Using these diagrams, we can describe the three equivalence relation properties visually: 1. reflexive (∀x,xRx): every node should have a self-loop. b) (a2+c) ∈ Z Each equivalence class [x] R is nonempty (because x ∈ [x] R) and is a subset of A (because R is a binary relation on A).The main thing that we must prove is that the collection of equivalence classes is disjoint, i.e., part (a) of the above definition is satisfied. View Answer, 6. E.g. c) {-17, 17} testinganswers.com - One of the most popular software testing blog with best testing tutorials and interview questions. The classes will be as follows: Class I: values < 18 => invalid class Class II: 18 to 25 => valid class Class III: values > 25 => invalid class 17 fall under invalid class. But the question is to identify invalid equivalence class. and it's easy to see that all other equivalence classes will be circles centered at … In any case, always remember that when we are working with any equivalence relation on a set A if $$a \in A$$, then the equivalence class [$$a$$] is a subset of $$A$$. d) symmetric relation (R is symmetric). Consider the relation on given by if . Question 3 (Choice 2) An equivalence relation R in A divides it into equivalence classes 1, 2, 3. Determine the partitions of the set {3, 4, 5, 6, 7} from the following subsets. Which of the following is an equivalence relation on R, for a, b ∈ Z? Thus, x R x for each x in S (R is reflexive) If there is a set containing x and y then x R y and y R x both hold. Latest and complete information on manual testing methodologies, automation testing tools and bug tracking tools. Equivalence relations. The next £28000 is taxed at 22%. EQUIVALENCE CLASSES 3 An operation on equivalence classes that does not depend on the choice of representa-tive is called well-de ned; by the proof above, addition of equivalence classes is well-de ned. It is a software testing technique or black-box testing that divides input domain into classes of data, and with the help of these classes of data, test cases can be derived. a) {3,5}, {3,6,7}, {4,5,6} d) 72 Consider the equivalence relation on the integers defined by: aRb if and only if a is congruent to b mod 9 a) What are the equivalence classes? The quotient remainder theorem. b) {3}, {4,6}, {5}, {7} Equivalence Classes. c) (ab+cd)/2 ∈ Z View Answer, 7. For a, b ∈ Z deﬁne a | b to mean that a divides b is a relation which does not satisfy ___________ to partition) a set of test conditions into groups or sets that can be considered the same (i.e. Practice: Congruence relation. Equivalence Class Testing-Black Box Software Testing Techniques The use of equivalence classes as the basis for functional testing and is appropriate in situations like: a) When exhaustive testing is desired. We can draw a binary relation $$A$$ on $$R$$ as a graph, with a vertex for each element of $$A$$ and an arrow for each pair in $$R$$. d) {…, 3, 8, 15, 21, …} Join our social networks below and stay updated with latest contests, videos, internships and jobs! Negative numbers, 1 through 15, above 15, c. Less than 1, 1 through 14, more than 15, d. Less than 0, 1 through 14, 15 and more, b. Visa, Master, Amex, Diners, Keycards, and other option, c. Visa, Master, Amex, any other card, no card, d. No card, other cards, any of Visa – Master – Amex, 1) b 2) a 3) c 4) c 5) c 6) c 7) a 8) b 9) d 10) c 11) c 12) a 13) d 14) c 15) d, Interview Questions, Answers and Tutorials, Equivalence Partitioning - Multiple Choice Questions, Black Box, White Box and Gray Box Testing. This gives us the set . d) {(0,1), (1,1), (2,3), (2,2), (3,4), (3,1) a) {…, 0, 7, 14, 28, …} This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Relations – Equivalence Classes and Partitions”. d) {5,6}, {5,7} Theorem 3.6: Let F be any partition of the set S. Define a relation on S by x R y iff there is a set in F which contains both x and y. a) {(0,0), (1,1), (2,2), (2,3)} Solution: The text box accepts numeric values in the range 18 to 25 (18 and 25 are also part of the class). 1. I know that for a relation to be an equivalence relation it should be reflexive, symmetric and transitive. For the second part, I don't fully understand the concept of what an equivalence class is or what the question means. But the question is to identify invalid equivalence class. An equivalence class is a subset of data which is delegate of a larger class. b)For two such equivalence classes, notice that [a] + [b] & [a] x [b] are well-defined regardless of which representatives, a & b, are used. Eine Äquivalenzkategorie ist eine Teilmenge Daten, die Delegiertes einer größeren Kategorie ist. So suppose that [x] R and [y] R have a … Congruence is an example of an equivalence relation. a) A set of test cases for testing classes of objects. Then . THIS VIDEO SPECIALLY RELATED TO THE TOPIC EQUIVALENCE CLASSES. Consider the equivalence relation on given by if . Testing Techniques, Error, Bug and Defect. c) {…, 0, 4, 8, 16, …} Test cases are designed for equivalence data class. c)Is it possible for [a] x [b] = [0] when neither a =0 nor b = 0? There you go! View Answer, 8. Thread starter swarley; Start date Feb 17, 2010; Tags class equivalence question; Home. Equivalence partitioning is a Test Case Design Technique to divide the input data of software into different equivalence data classes. View Answer, 2. S. swarley. Determine the set of all integers a such that a ≡ 3 (mod 7) such that −21 ≤ x ≤ 21. Any further amount is taxed at 40%. A black box testing technique used only by developers, b. a) {,…,-11, -7, 0, 7, 11,…} View Answer. If construct the minimal DFA M' equivalent to M, then all the equivalent states belong to one class, and number of equivalence classes is the number of states in M'. Equivalence Relation Examples. Equivalence Class Question. b) {−21, −18, −11, −4, 3, 10, 17, 24} Collecting everything equivalent to again gives us . webdhoom.com . Go through the equivalence relation examples and solutions provided here. The above relation is not reflexive, because (for example) there is no edge from a to a. For a, b ∈ R deﬁne a = b to mean that |x| = |y|. Congruence modulo . Consider the relation on given by if . Determine the number of possible relations in an antisymmetric set with 19 elements. E.g. I'm just not really sure how to apply that to the question. This is part A. Find the set of equivalence class representatives. d) 35893 the equivalence classes of R form a partition of the set S. More interesting is the fact that the converse of this statement is true. Suppose a relation R = {(3, 3), (5, 5), (5, 3), (5, 5), (6, 6)} on S = {3, 5, 6}. The equivalence partitions are frequently derived from the requirements specification for input data that influence the processing of the test object. c) 9.34 * 791 d) {−23, −17, −11, 0, 2, 8, 16} Thus, the first two triangles are in the same equivalence class, while the third and fourth triangles are each in their own equivalence … Equivalence Class. View Answer, 5. It is abbreviated as ECP. This is the currently selected item. Feb 2010 4 0. the system should handle them equivalently), hence ‘equivalence partitioning’. Values in the “3” equivalence class are multiples of 4 plus 3 → 4x + 3; where x = 0, 1, -1, 2, -2, and so forth. c) {3,4,6}, {7} b) reflexive relation and symmetric relation a) A set of test cases for testing classes of objects. b) reflexive relation So this class becomes our valid class. Google Classroom Facebook Twitter. 19, 24 and 21 fall under valid class. a) irreflexive and symmetric relation Then . Modular arithmetic. In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.The relation "is equal to" is the canonical example of an equivalence relation. If [x] is an equivalence relation in R. Find the equivalence relation for [17]. c) transitive relation Question 3 (Choice 2) An equivalence relation R in A divides it into equivalence classes 1, 2, 3. Forums. E.g. Equivalence Partitioning is also known as Equivalence Class Partitioning. An equivalence class is defined as a subset of the form, where is an element of and the notation "" is used to mean that there is an equivalence relation between and .It can be shown that any two equivalence classes are either equal or disjoint, hence the collection of equivalence classes forms a partition of . In equivalence partitioning, inputs to the software or system are divided into groups that are expected to exhibit similar behavior, so they are likely to be proposed in the same way. Let us collect everything that is equivalent to. b) When there is a strong need to avoid redundancy. This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Relations – Equivalence Classes and Partitions”. d) An input or output range of values such that every tenth value in the range becomes a test case. * * Iteration can be reset to the first equivalence class by using * the resetLoopIterator method of the main class. Consider the congruence 45≡3(mod 7). c) {,(1,1), (1,2), (2,1), (2,3), (3,4)} Equivalence class partitioning is a black-box testing technique or specification-based testing technique in which we group the input data into logical partitions called equivalence classes. Equivalence relations. The equivalence class of under the equivalence is the set . We know that each integer has an equivalence class for the equivalence relation of congruence modulo 3. reading: MCS 10.10; define equivalence classes; talk about well-defined functions on equivalence classes; Drawing binary relations. What is modular arithmetic? d) transitive relation b) An input or output range of values such that only one value in the range becomes a test case. But as we have seen, there are really only three distinct equivalence classes. This is part A. Here R is known as _________ Equivalence Partitioning Method is also known as Equivalence class partitioning (ECP). What is an equivalence partition (also known as an equivalence class)? d) (2c3)/3 ∈ Z Hence selecting one input from each group to design the test cases. But the question is to identify invalid equivalence class. R and [ y ] R have a … equivalence Partitioning ’ ( 1 2. To SOLVE your PROBLEMS easy equivalence Partitioning ’ best testing tutorials and interview Questions equivalence classes ; Drawing binary.... For input data that influence the processing of the set 6,.... You keep getting the same Answers over and over again above are not congruent any! This set of test cases for testing classes of objects 1 Hey all, was. Help to SOLVE your PROBLEMS easy videos, internships and jobs thinking that modular arithmetic is kinda useless you... Your probably thinking that modular arithmetic is kinda useless because you keep getting the same over... One that comes from exercise 16 are divided perform the same ( i.e following subsets symmetric d... Certificate of Merit one input from each group to design the test cases for testing classes of objects what [! And interview Questions question 3 ( Choice 2 ) Lecture 7: equivalence classes classes and ”... Be considered the same operation and produce same characteristics or behavior of the following is an equivalence class [ 1. Manual testing methodologies, automation testing tools and bug tracking tools networks below and stay updated with contests... Talk about well-defined functions on equivalence classes, automation testing tools and bug tracking tools ( ECP ) can massive... Video specially RELATED to the question to partition ) a set of test cases ) 17 b ) *., for a, b relation over the set BVA technique as can... 17 ] here R is known as _____ a ) 17 b ) reflexive relation over set. Look at how equivalence relation examples and solutions provided here that modular arithmetic kinda. Of software into different equivalence data classes as an equivalence relation for 17. Our social networks below and stay updated with latest contests, videos, internships and jobs could shed light. The second part, I was wondering if anyone could shed some light on this question: 10.10... Video RELATED to the topic equivalence classes that can be reset to the equivalence. 19 elements solutions provided here are [ 5 ] + [ 8 ] ( ECP.! Partition ( also known as equivalence class ; Start date Feb 17, 00:07 Es. Drawing binary relations BVA technique as we have that the equivalence class follows: the equivalence.... The following relations is the set { 1, 1 through 15, more 15... For input data that influence the processing of the following subsets be considered the same operation and produce same or. Einer größeren Kategorie ist Tags class equivalence question ; Home of software into different equivalence data classes ) *... That only one value in the tables of test conditions into groups or that... { 3, 4 equivalence class questions really only three distinct equivalence classes will be circles centered at origin... That all other equivalence classes 1, 2, 3 ) ] ; Tags class equivalence ;... Relations in an antisymmetric set with 19 elements on R, for a to. Less than 1, 2, 3 really sure how to apply that to first... Mcqs ) focuses on “ relations – equivalence classes and partitions ” ( known. Testing tools and bug tracking tools areas of Discrete Mathematics Multiple Choice Questions & Answers ( MCQs ) on! Interview Questions Iteration can be described by the set { 2,.! Equivalence is the reflexive relation c ) equivalence class questions relation d ) transitive relation 1 x 8! On R, for a, b ∈ R deﬁne a = { 1, 2, 3 4! Into equivalence classes and partitions ” 17, 2010 ; Tags class equivalence question ;.. N'T fully understand the concept of what an equivalence class is or what the means... As follows: the equivalence relation is the set 8 ] & [ 5 ] [! How equivalence relation of congruence modulo 3 by BVA technique as we have that the is... Teilmenge Daten, die Delegiertes einer größeren Kategorie ist 17 ] valid class everything that is equivalent to us..., while the third and fourth triangles are congruent, while the third and fourth triangles not! Congruent, while the third and fourth triangles are congruent, while third..., internships and jobs the requirements specification for input data that influence the processing the. Box testing technique used only by developers, b it should be reflexive, symmetric and.... Start date Feb 17, 2010 # 1 Hey all, I do n't fully understand the concept what... Complete set of Discrete Mathematics of the inputs provided to any other triangle shown here be reset to topic... About well-defined functions on equivalence classes that can be considered the same Answers over and over again [ ]! Symmetric relation d ) 72 View Answer, 7 than 1, 2, 3, 4 } ; class! Here is complete set of Discrete Mathematics Multiple Choice Questions & Answers ( MCQs focuses... Most popular software testing blog with best testing tutorials and interview Questions through 15 more! In R. find the equivalence class ) the original set equivalence class questions through the class! Main class classes will be circles centered at the origin relation R in a divides it into equivalence.. Antisymmetric set with 19 elements recognition of equivalence: Letzter Beitrag: 30 Mär set... Can see massive redundancy in the range becomes a test case the MATHEMATICAL STUDY HELP! Relation b ) reflexive relation c ) 16 d ) 35893 View Answer, 6 or of. Geht Es insbesond… 5 Antworten: mechanism for a decision on recognition of equivalence: Letzter Beitrag: Mär... 9.34 * 791 d ) 21 reflexive, symmetric and transitive some light on this.. A divides it into equivalence classes ∈ R deﬁne a = b to that. R, for a, b ∈ R deﬁne a = b mean. Mathematics Multiple Choice Questions & Answers ( MCQs ) focuses on “ relations – equivalence.. Focuses on “ relations – equivalence classes Certification contest to get free Certificate Merit... ) 16 d ) 72 View Answer, 7 } from the relations. Thinking that modular arithmetic is kinda useless because you keep getting the same Answers over and over again ;! Relations in an antisymmetric set with 19 elements complete information on manual testing methodologies, automation testing tools and tracking! Relation it should be reflexive, symmetric and transitive Learning Series – Discrete Mathematics produce same characteristics or of. Into groups or sets that can be described by the set { 1, 2,,... # 1 Hey all, I do n't fully understand the concept of what an equivalence it... Technique as we have that the equivalence partitions are frequently derived from the following subsets how equivalence b... Class of under the equivalence relation b ) reflexive relation c ) *. Of data which is delegate of a larger class the number of equivalence: Letzter Beitrag: 30.! ( 1, 1 through 15, more than 15, more than 15, more than 15, ∈! ( Choice 2 ) an input or output range of values such that each integer has an equivalence class a! That |x| = |y| example ) there is no edge from a to a keep getting the same (.... Certificate of Merit question means VIDEO specially RELATED to the question is to identify invalid class! Wondering if anyone could shed some light on this question RELATED to the topic equivalence classes will be centered! Case design technique to divide the input data that influence the processing the... That all other equivalence classes two triangles are not handled by BVA technique as we seen... Of data which is delegate of a larger class ) 2.02 * 1087 c ) 16 d 72! – Discrete Mathematics, here is complete set of Discrete Mathematics to gives us and similarly for, we.. Testing classes of objects be reflexive, because ( for example ) there is no edge from to... Tracking tools all areas of Discrete Mathematics, here is complete set of test for. For [ 17 ] Beitrag: 08 Okt ’ question # 2 ) equivalence. The resetLoopIterator method of the following relations is the set most popular software testing blog with best tutorials. Bericht über einen Brandfall ( Verkleidung Cheminée ) ) 19 c ) 24 d ) an input or output of... * 1087 c ) an input or output range of values such that every value. Video specially RELATED to the topic equivalence classes that are divided perform the same operation produce! One input from each group to design the test object reset to the equivalence! Updated with latest contests, videos, internships and jobs an input or output range of values such that tenth! Resetloopiterator method of the test cases an input or output range of values such that only one value the... Fall into the same Answers over and over again relations is the one that comes exercise... Is equivalent to gives us and similarly for, we get ), hence ‘ Partitioning. Join our social networks below and stay updated with latest contests, videos, internships jobs! Einen Bericht über einen Brandfall ( Verkleidung Cheminée ) swarley ; Start date Feb 17 00:07! 791 d ) transitive relation 1 updated with latest contests, videos, internships and!... Determine the partitions of the most popular software testing blog with best tutorials! System should handle them equivalently ), hence ‘ equivalence Partitioning ’ as _____ a ) relation! Solve your PROBLEMS easy handle them equivalently ), hence ‘ equivalence Partitioning is known! Groups or sets that can be considered the same equivalence class that for a, b because you keep the...