Question

1) Consider a relation R(A,B) with r tuples, all unique within R, and a relation S(B,C) with s tuples, all unique within S. Let t represent the number of tuples in R natural-join S. What is the value range of t? What is the value of t for R natural-join R (assuming no null values in R)? Explain your answer.

Answer 1

case 1:
Relation R (A,B)
Let R has 2 tuple
A   B
1   2
2   2

Relation S (B,C)
Let S has 3 tuple
B   C
1   2
1   3
3   4

When we do natural join over R and S ,we get 0 Tuples.
Hence minimum number of tuples =0

case 2:
Relation R (A,B)
Let R has 2 tuple
A   B
1   2
2   2

Relation S (B,C)
Let S has 3 tuple
B   C
2   2
2   3
2   4

When we do natural join over R and S
A B C
1 2 2
1 2 3
1 2 4
2 2 2
2 2 3
2 2 4

Total 6 tuples (2*3).

Relation R(A,B) with r tuples, all unique within R, and a Relation S(B,C) with s tuples, all unique within S

range of tuple = 0 to r*s