Consider the join of a relation R , with a relation S . If R has m number of tuples and S has n number of tuples then the maximum and minimum sizes of the join respectively are:
(A)
m + n & 0
(B)
mn & 0
(C)
m + n & | m – n |
(D)
mn & m + n
Answer: (B)
Explanation:
Consider the following examples:
Case 1: Maximum tuples- When the common attribute contains identical values
Relation R Relation S R ⋈ S
a b a d a b d
1 2 1 10 1 2 10
1 3 1 11 1 2 11
1 4 1 3 10
1 3 11
1 4 10
1 4 11Case 2: Minimum Tuples- When Both the relations have a common attribute but no tuple in both relations match.
Relation R Relation S R ⋈ S
a b a d a b d
1 2 2 10 No tuple
1 3 3 11
1 4
So, option (B) is correct.
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