Testing Lossless join

Question

State true or false:-

Symbol " ^ " stands for an intersection AND letters in bold are the candidate key of the respective table.

1)  R1(A, B, C) ^ R2(B, C) = {B,C} IS LOSSLESS JOIN.

2)  R1(A, B, C) ^ R2(B, D) = {B} IS LOSSY JOIN.

3)  R1(A, B, C) ^ R2(B, C) = {B,C} IS LOSSLESS JOIN.

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state whether the given decomposition is lossless-join decomposition or not:-

letters in bold are the candidate key of the respective table.

Relation R(A, B, C, D, E, F, G) is decomposed into

R1(A, B, C), R2(D, E), R3(F, B), R4(D, G, A)

Also, tell what will be the candidate key after performing join each time and at the end.

Answer 1

R1(A, B, C), R2(D, E), R3(F, B), R4(D, G, A)

R1(A, B, C) and R3(F, B) can be joined R5(A,B,C,F)

R2(D, E) and R4(D, G, A) can be joined R6(A,D,E,G)

R5(A,B,C,F) and R6(A,D,E,G) can be joined R(A,B,C,D,E,F,G)---AG will be the candidate key

Comments

In R5 how you choose A as cand key and in R6 G as cand Key and in the final relation also AG is cand key ?

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see in R5 A->BC , B->F are the functional dependencies so it will give rise to A->BCF similarly you can work out with other things