Question

Given a module which implements the function Z= F(X, Y), defined as follows:

         X + Y when 10<=X<=20, and 12<=Y<=30

Z =    X - Y when 0<=X<10, and 0<=Y<12      

          0 under other conditions

          where X and Y are integer parameters for F.

1. Identify the equivalence classes in [X, Y].

2. List your test cases in [X, Y] based on your equivalence class analysis.

Answer 1

Answer 1:
Equivalence class is a subset which include all the elements equivalent to each other i.e. any element from that subset will give the same result. There are following equivalent classes in [X,Y]:
a. X<0;
  Y Z (X is any negative integer, Y belongs to any integer) result will be 0
Note, Z is the notation for integers
b. X [ 0, 10);
  Y [ 0, 12 ) (X is any integer greater than equal to 0 and less than 10, Y belongs to any integer greater than equal to 0 and less than 12) result will be (X-Y)
c. X [ 0, 10);
  Y Z except [ 0, 12 ) (X is any integer greater than equal to 0 and less than 10, Y belongs to any integer less than 0 or greater than equal to 12) result will be 0
d. X [ 10, 20];
  Y [ 12, 30 ] (X is any integer greater than equal to 10 and less than equal to 20, Y belongs to any integer greater than equal to 12 and less than equal to 30) result will be (X+Y)
e. X [ 10, 20];
Y Z except [ 12, 30 ] (X is any integer greater than equal to 10 and less than equal to 20, Y belongs to any integer less than 12 or greater than 30) result will be 0
f. X > 20;
Y Z (X is any integer greater than 20, Y belongs to any integer) result will be 0

Answer 2:
Test cases in [X, Y] will include one element from each class defined above. Therefore, there will be following 6 test cases: (there are multiple answers possible to this question)
1.  [X,Y] = [-2, 30] ...
2.  [X,Y] = [3, 9] ...
3.  [X,Y] = [3, 12] ...
4.  [X,Y] = [10, 12] ...
5.  [X,Y] = [12, 8] ...
6.  [X,Y] = [30, -6] OR  [30, 60] ....