In this paper, in the first we introduce the concept of algebra of the power set and new notions connected to it are investigated and discussed like subalgebra of the power set, soft algebra of the power set and soft subalgebra of the power set. Then some binary operations between two soft algebras of the power set are studied. Further, we state the relations between soft algebra of the power set and soft algebra of the power set. Moreover, several examples are given to illustrate the notations introduced in this work.
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