1
GATE CSE 2022
MCQ (More than One Correct Answer)
+1
-0.33

Consider the following three relations in a relational database.

Employee ( $$\underline {eld}$$ , Name), Brand ( $$\underline {bld}$$ , bName), Own ( $$\underline {eld}$$ , $$\underline {bld}$$)

Which of the following relational algebra expressions return the set of elds who own all the brands?

A
$$\pi$$eld ($$\pi$$eld, bld (Own) / $$\pi$$bld (Brand))
B
$$\pi$$eld (Own) $$-$$ $$\pi$$eld (($$\pi$$eld (Own) $$\times$$ $$\pi$$bld (Brand)) $$-$$ $$\pi$$eld, bld (Own))
C
$$\pi$$eld ($$\pi$$eld, bld (Own) / $$\pi$$bld (Own))
D
$$\pi$$eld (($$\pi$$eld (Own) $$\times$$ $$\pi$$bld (Own) / $$\pi$$bld (Brand))
2
GATE CSE 2014 Set 3
+1
-0.3
What is the optimized version of the relation algebra expression $$\pi_{A1}(\pi_{A2}(\sigma_{F1}(\sigma_{F2}(r))))$$, where $$A1, A2$$ are sets of attributes in r with $$A1 \subset A2$$ and $$F1,F2$$ are Boolean expressions based on the attributes in r?
A
$$\pi_{A1}(\sigma_{(F1 \wedge F2)}(r))$$
B
$$\pi_{A1}(\sigma_{(F1 \vee F2)}(r))$$
C
$$\pi_{A2}(\sigma_{(F1 \wedge F2)}(r))$$
D
$$\pi_{A2}(\sigma_{(F1 \vee F2)}(r))$$
3
GATE CSE 2008
+1
-0.3

Which of the following tuple relational calculus expression(s) is/are equivalent to $$\forall t \in r \left(P\left(t\right)\right)$$?

I. $$\neg \exists t \in r \left(P\left(t\right)\right)$$
II. $$\exists t \notin r \left(P\left(t\right)\right)$$
III. $$\neg \exists t \in r \left(\neg P\left(t\right)\right)$$
IV. $$\exists t \notin r \left(\neg P\left(t\right)\right)$$
A
I only
B
II only
C
III only
D
III and IV only
4
GATE CSE 2006
+1
-0.3
Consider the relations r1(P, Q, R) and r2(R, S, T) with primary keys P and R respectively. The relation r1 contains 2000 tuples and r2 contains 2500 tuples. The maximum size of the join $${r_1} \Join {r_2}$$ is
A
2000
B
2500
C
4500
D
5000
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