Prove that, if r and s are union-compatible, then r ? s = r  s.

What will be an ideal response?


Because r and s are union-compatible, the attributes of r and s are the same. Let them be A1,...,A. Thus:
r  s = ?A1n,...,An(?A1=A1 AND A2=A2 AND ... AND An=An(r × s))

Since r and s are relations over A1,...,An, it means that only the tuples that are both in r and s survive the selection, i.e., the result is the intersection of the two relations.

Computer Science & Information Technology

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