Multiple choice

Let R and S be relational schemes such that R={a,b,c} and S={c}. Now consider the following queries on the database:

I. $\pi_{R-S}(r) - \pi_{R-S} \left (\pi_{R-S} (r) \times s - \pi_{R-S,S}(r)\right )$ II. $\left\{t \mid t \in \pi_{R-S} (r) \wedge \forall u \in s \left(\exists v \in r \left(u = v[S] \wedge t = v\left[R-S\right]\right )\right )\right\}$ III. $\left\{t \mid t \in \pi_{R-S} (r) \wedge \forall v \in r \left(\exists u \in s \left(u = v[S] \wedge t = v\left[R-S\right]\right )\right ) \right\}$ IV.

Select R.a, R.b
            From R,S
            Where R.c=S.c

Which of the above queries are equivalent?

  1. I and II

  2. I and III

  3. II and IV

  4. III and IV

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation