Object-Oriented Programming Assignment
Introduction -
"A logical matrix or (0, 1) matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a matrix can be used to represent a binary relation between a pair of finite sets. If R is a binary relation between the finite indexed sets X and Y (so R ⊆ X×Y), then R can be represented by the logical matrix M whose row and column indices index the elements of X and Y, respectively, such that the entries of M are defined by:
In order to designate the row and column numbers of the matrix, the sets X and Y are indexed with positive integers: i ranges from 1 to the cardinality (size) of X and j ranges from 1 to the cardinality of Y.
Define a class (called LogMat) to represent logical matrix of any binary relation as explained previously.
A. The class has three member variables: matrix (as dynamic 2-D array), rowSize and columnSize.
B. Provide a default constructor with default parameter to initialize an empty matrix to 0 with a maximum of 10 X 10.
C. Overload the stream extraction (>>) to read the R from input file where the format of the input file as {(1, 1), (1, 2), (1, 3), (1, 4), (2, 2), (2, 4), (3, 3), (4, 4)} for each R.
D. Overload the stream insertion (<<) to display the matrix on the screen.
E. Overload the (==) operator to check if two sets are equal.
F. Overload the plus (+) operator to return the combination between two sets. For example if A and B are sets then A + B should return a set that contains all the elements in either or both of the sets.
G. Provide functions that should/must be in the class.
H. Write main program that:
i. Create an input file for each of the below relations:
- aRb holds if and only if a divides b evenly, with no remainder
- aRb holds if and only if the sum of a+b is an even number.
ii. Each set should be in format as mentioned in part C.
iii. Create at least one object for each relation.
iv. Test the operators the overloaded operators.