Definition of relational algebra

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The division operator of relational algebra, "÷", is defined as follows. Let r(R) and s(S) be relations, and let S ⊆ R; that is, every attribute of schema S is also in schema R. Given a tuple t, let t[S] denote the projection of tuple t on the attributes in S. Then r ÷ s is a relation on schema R - S (that is, on the schema containing all attributes of schema R that are not in schema S). A tuple t is in r ÷ s if and only if both of the following conditions hold:- t is in ΠR-S(r)- For every