# GATE | GATE CS 2010 | Question 43

Which of the following functional dependencies hold for relations R(A, B, C) and S(B, D, E):

```B -> A
A -> C```

The relation R contains 200 tuples and the rel ation S contains 100 tuples. What is the maximum number of tuples possible in the natural join of R and S (R natural join S)
(A) 100
(B) 200
(C) 300
(D) 2000

Explanation:

From the given set of functional dependencies, it can be observed that B is a candidate key of R. So all 200 values of B must be unique in R. There is no functional dependency given for S. To get the maximum number of tuples in output, there can be two possibilities for S.
1) All 100 values of B in S are same and there is an entry in R that matches with this value. In this case, we get 100 tuples in output.
2) All 100 values of B in S are different and these values are present in R also. In this case also, we get 100 tuples.

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