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The following functional dependencies hold for relations R(A, B, C) and S(B, D, E)
B → A,
A → C
The relation R contains 200tuples and the relation S contains 100tuples. What is the maximum number of tuples possible in the natural join R⋈S ?
  • a)
    100
  • b)
    200
  • c)
    300
  • d)
    2000
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The following functional dependencies hold for relations R(A, B, C) an...
For given relation R1(A, B, C) and R2(B, D, E), functional dependencies are given only for relation R1, not for R2 And the candidate key for R1 is B, so all values must be unique in R1. To get the maximum number of tuples in output, there can be two possibilities.
1) All 100 values of B in R2 are the same and there is an entry in R1 that matches with this value. In this case, we get 100 tuples in output.
Example:
Consider an example, suppose there is two tables R1(A, B, C) consisting of 5 tuples and R2( B, D, E) consisting of 4 tuples only.



Natural join of R1 and R2 (R1 * R2) gives: 4
2) All 100 values of B in R2 are different and these values are present in R1 also. In this case, also we get 100 tuples.
Example:
Consider an example, suppose there is two tables R1(A, B, C) consists of 5 tuples and R2( B, D, E) consists of 4 tuples only.


Natural join of R1 and R2 (R1 * R2) gives: 4
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Community Answer
The following functional dependencies hold for relations R(A, B, C) an...
It seems like the functional dependencies are missing. Please provide the functional dependencies for relations R(A, B, C) and S(B, D, E).
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The following functional dependencies hold for relations R(A, B, C) and S(B, D, E)B → A,A → CThe relation R contains 200tuples and the relation S contains 100tuples. What is the maximum number of tuples possible in the natural join RS ?a)100b)200c)300d)2000Correct answer is option 'A'. Can you explain this answer?
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