Object-Oriented Programing 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:

           1  (x_i, y_j) ∈ R

M i,j =

            0  (x_i, y_j) ∉ R

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.

Example:

The binary relation R on the set {1, 2, 3, 4} is defined so that aRb holds if and only if a divides b evenly, with no remainder. For example, 2R4 holds because 2 divides 4 without leaving a remainder, but 3R4 does not hold because when 3 divides 4 there is a remainder of 1. The following set is the set of pairs for which the relation R holds.

{(0,0), (1,0), (2,0), (3,0), (4,0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 2), (2, 4), (3, 3), (4, 4)}.

The corresponding representation as a Boolean matrix is:

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.