ISRO | ISRO CS 2016 | Question 49

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    11

Case 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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