Some Formulae for the Number of SDRs and Symbolic Representations

If (Ai:1 ⩽ i ⩽ n) is a family of n finite sets, then two expressions for the number of SDRs for this family are obtained in terms of the cardinalities of unions and symmetric differences respectively. The proof makes use of the already known expression in terms of intersections. For this known expression is given a symbolic representation in the form of a determinant defined in a special manner. Also a representation, again as a determinant, for the number of SDRs in terms of the complements of the sets Ai is given