Question

Suppose that R(A,B,C) and S(B,C) are bags. R has three tuples (1,1,4), (3,4,2), (2,2,3). S has two tuples (1,4), (2,3). Which of the following is a result of a expression: δ(γA, SUM(B)->SUMB(δ(R*S))) (Note that: the notation * denotes for the natural join)

Select one:
a. two tuples
b. one tuples
c. the expression is invalid
d. three tuples

Answer 1

The expression δ(γA, SUM(B)->SUMB(δ(R*S))) is invalid and results in three tuples.

Step-by-step explanation:

The expression δ(γA, SUM(B)->SUMB(δ(R*S))) is invalid.

Let's break down the expression:

1. R*S represents the natural join of relations R and S, which yields the tuples (1,1,4,1,4), (3,4,2,2,3), and (2,2,3,2,3).
2. δ(R*S) performs a duplicate elimination operation on the tuples, resulting in (1,1,4,1,4), (3,4,2,2,3), and (2,2,3,2,3).
3. SUM(B) computes the sum of the B attribute for each tuple, giving the values 4, 7, and 4.
4. δ(γA, SUM(B)) performs a duplicate elimination on the A and SUM(B) attributes, resulting in (1, 4), (3, 7), and (2, 4).
5. Since the δ(γA, SUM(B)) operation only considers the A attribute, the tuples (1, 4), (3, 7), and (2, 4) are selected from the previous result.

Therefore, the result of the expression is (1, 4), (3, 7), and (2, 4), which is three tuples.