. . Some binary operations on Boolean Matrices Definition . A Boolean Matrix is a real matrix whose entries are either or .
Note that the boolean entries and can be defined in several ways. In electrical switch to describe “on and off”, in graph theory, the “adjacency matrix” etc , the boolean entries and are used. We consider the same type of Boolean matrices in our discussion. The following two kinds of operations on the collection of all boolean matrices are defined.
Let A a ij = and B b ij = be any two boolean matrices of the same type . Then their join ∨ and meet ∧ are defined as follows: Definition . : Join of A and B A B