of equivalence classes of ˘forms a partition of X. Theorem 2: Suppose C P(X) is a partition of a set X. }\) Equivalence relations give rise to partitions. For instance, .
Equivalence partitions are also known as equivalence classes – the two terms mean exactly the same thing. As we run over each element of the set , each element lies in one and only one of the equivalence classes so that the union of the equivalence classes will contain each element of the set (i.e.

Partitions If S is a set with an equivalence relation R, then it is easy to see that 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. Normally Boundary value analysis is part of stress and negative testing. Eg.

As a real-world example, consider a deck of playing cards. A boundary value is an input or output value on the border of an equivalence partition, includes minimum and maximum values at inside and outside boundaries. Let us consider a program that separates integers into positive or negative. 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. So every equivalence relation partitions its set into equivalence classes. There is a close relation between partitions and equivalence classes since the equivalence classes of an equivalence relation form a partition of the underlying set, as will be proven in Theorem 7.18. The congruence class of 1 modulo 5 (denoted ) is .
There is a close relation between partitions and equivalence classes since the equivalence classes of an equivalence relation form a partition of the underlying set, as will be proven in Theorem 7.18. A boundary value is an input or output value on the border of an equivalence partition, includes minimum and maximum values at inside and outside boundaries. Thus, ∼ is an equivalence relation with , ∈ as the equivalence classes. It is abbreviated as ECP. Lastly obtaining a partition P {\displaystyle P} from ∼ {\displaystyle \sim } on X {\displaystyle X} and then obtaining an equivalence equation from P {\displaystyle P} obviously returns ∼ {\displaystyle \sim } again, so ∼ {\displaystyle \sim } and P {\displaystyle P} are equivalent structures. Let \(\sim\) be an equivalence relation on the nonempty set \(A\). Equivalence Class Testing, which is also known as Equivalence Class Partitioning (ECP) and Equivalence Partitioning, is an important software testing technique used by the team of testers for grouping and partitioning of the test input data, which is then used for the purpose of testing the software product into a number of different classes. And accepts any number between -5 and + 5. Then the relation ˘on X de ned by x ˘y ()(9C 2C)(x;y 2C) is an equivalence relation. Theorem 7.18. Boundary value analysis is a test case design technique to test boundary value between partitions (both valid boundary partition and invalid boundary partition). Equivalence Partitioning. The Below example best describes the equivalence class Partitioning: Assume that the application accepts an integer in the range 100 to 999 Valid Equivalence Class partition: 100 to 999 inclusive. Notice that in each case, the cells of the partition are the equivalence classes of the set under the corresponding equivalence relation. Consequently, we may consider a partition of a set as a way of dividing up into distinct, non-overlapping pieces. Alphabets, Numbers , range of numbers etc . Theorem 7.18. It can be shown that any two equivalence classes are either equal or disjoint, hence the collection of equivalence classes forms a partition of X.