TABLES OF D-CLASSES IN THE SEMIGROUP $B_n1$ OF THE BINARY RELATIONS ON A SET X WITH n-ELEMENTS

TABLES OF D-CLASSES IN THE SEMIGROUP $B_n1$ OF THE BINARY RELATIONS ON A SET X WITH n-ELEMENTS

M$_{n}$(F) denotes the set of all n*n matrices over F={0, 1}. For a, b.mem.F, define a+b=max{a, b} and ab=min{a, b}. Under these operations a+b and ab, M$_{n}$(F) forms a multiplicative semigroup (see [1], [4]) and we call it the semigroup of the n*n boolean matrices over F={0, 1}. Since the semigroup M$_{n}$(F) is the matrix representation of the semigroup B$_{n}$ of the binary relations on the set X with n elements, we may identify M$_{n}$(F) with B$_{n}$ for finding all D-classes.l D-classes.

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