Advanced Database Management System - Tutorials and Notes: Result of set difference operator in relational algebra

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Thursday, 8 September 2016

Result of set difference operator in relational algebra

Result of a set difference operator in relational algebra


Question:


6. Which of the following is equivalent to the expression R - (R - S)?

(a) R
(b) S
(c) R - S
(d) R ∩ S



Answer:

(d) R ∩ S

R - (R - S) is equivalent to R ∩ S . This could be understood from the following example;



Let us take the following tables (relations) R and S with 3 and 2 tuples respectively.
R

B
D
Tuple 1
b1
d1
Tuple 2
b2
d2
Tuple 3
b3
d3

S

B
D
Tuple 1
b1
d4
Tuple 2
b3
d3

The following table shows R-S. The result contains all the records that are unique for R and not for S. In other words, the common tuple in R and S is removed and the tuples that are only part of R is retained.

R – S

B
D
Tuple 1
b1
d1
Tuple 2
b2
d2

The following table shows R-(R-S). The result contains records that are unique for R and not for (R-S).

R – (R – S)

B
D
Tuple 1
b3
d3

From the result, it is very clear that the tuple (b3, d3) is the common tuple that presents in both R and S. Hence, R-(R-S) is equivalent to R ∩ S.









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