Question

3 Given the relations R (A, B) and S (B, C) where values are all integers. Examine the undermentioned three relational algebra expressions: a. A, C(R⋈B=1S) b. A(B = 1R)XC(B = 1S) c. A, C (ARXB = 1S) Two of the three expressions are equivalent (i.e., they produce the same answer on all databases), while one of them can produce a different answer. 2.3.1 Which query can produce a contrasting answer? Give the simplest database instance you can think of where a different answer is produced. (5) 2.3.2 Why do we care that the expressions are equivalent? (5) 2.3.3 How can we determine that the expressions are equivalent? 

Answer 1

From the given option, we can conclude that query 1 produces the different result.

a) $\pi_{(A,C)}(\pi_AR \times \sigma_{B=1}S)$

b)

Let R = {(3, 4)} and S = {(1, 2)}

In this case, (a) and (b) produces empty result.

c)

In this, c produces {(3,2)}