UGC NET CSE | June 2016 | Part 3 | Question: 9

Question

Consider the relations $R(A, B)$ and $S(B, C)$ and the following four relational algebra queries over R ans S

1. $\pi_{A, B} (R \bowtie S)$
2. $R \bowtie \pi_B(S)$
3. $R \cap (\pi_A(R) \times \pi_B (S))$
4. $\Pi_{A. R. B} (R \times S)$ where $R.B$ refers to the column B in table R

One can determine that:

• A. I, III and IV are the same query
• B. II, III and IV are the same query
• C. I, II and IV are the same query
• D. I, II and III are the same query

Comments

In query no 4 there is no equal to condition  check  while in rest R.B=S.B is checked

hence ans is option d

Answer 1

I think answer is 4

Let us take an example as R= {(10,1),(20,2)} and S={(2,30),(3,40)}

I)  R⟗S= {(20, 2,30)}. So π _{A, B} R⟗S = {(20,2)}

II) π _B (S) ={(2),(3)}. So R⟗π _B (S) = {(20,2)}

III)  π _A (R) X π _B (S) ={10,20} X {2,3} ={(10,2),(10,3),(20,2),(20,3)}

R ∩ π _A (R) X π _B (S)={(20,2)}

IV) R X S = {(10,1,2,30),(10,1,3,40),(20,2,2,30),(20,2,3,40)}

π _{A, R.B} R X S ={(10,2),(10,3),(20,2),(20,3)}

Comments

In option IV , you are taking values of S.B instead of R.B, then how option iv wouldn't be equivalent to the rest of three options?

Answer 2

A option answer