Prove that relational algebra queries are domain-independent. Hint: Use induction on the structure of the relational algebra expression.
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The proof is by induction on the structure of algebraic expressions.
Base case: The expression is P, where P is a relation name. Clearly, the contents of the relation assigned to P in the database is ?xed and does not depend on the domain.
Inductive hypothesis: Assume that all expressions of length less than or equal to N are domain independent. We will prove that then any expression of length M +1 is domain independent.
We need to consider the various cases that correspond to each of the relational operators. In all cases, the reasoning is similar. For instance, let the query be E1 ? E2, where E1and E2 are relational expressions of smaller length. By inductive hypothesis,
they are domain independent. Clearly, then, their union is domain independent as well.
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