Verify that, for any pair of relations r and s, ? cond (r × s)=r × ? cond(s) if the selection condition cond involves only the attributes mentioned in the schema of relation s.

What will be an ideal response?


?cond(r × s)={< r , s > |r ? r, s ? s, < r , s > satis?es cond }.Since cond involves only the attribute in s, the requirement that < r , s > satis?es cond can be replaced with s satis?es cond . By de?nition of selection and cross product, r × ? cond(s)={< r , s >|r ? r, s ? s and s satis?es cond }. Hence, the two expressions are equivalent.

Computer Science & Information Technology

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