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Functional-Dependency Theory




Q. R = ( A, B, C, G, H, I ) and the set F of functional dependencies { A → B, A → C, CG → H, CG → I , B → H}.





Q. Find the possible functional dependencies in relation R, if n is the number of attributes in R.



Attribute Closure Algorithm



Q. For schema R = ( A, B, C, G, H, I ) and the set F of functional dependencies { A → B, A → C, CG → H, CG → I , B → H}. Compute (AG)+ which is closure of α under F .





Canonical Cover



Q. F contains AB → CD, A → E, and E → C. Check if C is extraneous in AB → CD.



Q. Consider that F contains AB → C, A → C. Check if B is extraneous in AB → C.



Q. F contains A → BC, B → C, and AB → D. What extraneous attributes are present in F.





Q. F contains A → BC, B → C, and AB → D. What extraneous attributes are present in F.




Canonical cover problems: Does F cover G




Q. Consider two sets of FD's such as F = {A → B, AB → C; D → AC; D → E} and G = {A → BC; D → AB}





Lossless decomposition



Test for checking 3NF



Q. R(ABCD) = F {AB → CD}





Q. R(ABCDE) = {AB → CD; E → A; D → A}



Q. R(ABCD) = {ABC → D; D → A}




Second Normal Form : 2NF




Q. R(ABCD) = {ABC → D; D → A}



Q. In a relation R(STUD_NO, COURSE_NO, COURSE_NAME) we have FD set: {COURSE_NO -> COURSE_NAME} and Candidate Key: {STUD_NO, COURSE_NO}



Q. R (A, B , C, D ) has FD set as AB -> C; BC -> D


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