Tuple Calculus
Q1.
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}(\pi_{R-S}(r) \times S -\pi_{R-S,S}(r)) II.\{t|t\in \pi _{R-S}(r)\wedge \forall u \in s (\exists v \in r(u=v[s]\wedge t=v[R-S]))\} III.\{t|t\in \pi _{R-S}(r)\wedge \forall v\in r(\exists u\in s(u=v[s]\wedge t=v[R-S]))\} IV. Select R.a, R.b From R,S Where R.c=S.c Which of the above queries are equivalent?Q2.
Consider the relation employee(name, sex, supervisorName) with name as the key. supervisorName gives the name of the supervisor of the employee under consideration. What does the following Tuple Relational Calculus query produce?Q3.
Consider a database that has the relation schemas EMP(EmpId, EmpName, DepId) and DEPT(DeptName, DeptId). Note that the DeptId can be permitted to be NULL in the relation EMP. Consider the following queries on the database expressed in tuple relational calculus. Which of the above queries are safe?Q4.
Which of the following tuple relational calculus expression(s) is/are equivalent to \forall t \in r(P(t))? I. \neg \exists t \in r(P(t)) II. \neg t \notin r(P(t)) III. \neg \exists t \in r(\neg P(t)) IV. \exists t \in r(\neg P(t))Q6.
A relation r(A,B) in a relational database has 1200 tuples. The attribute A has integer values ranging from 6 to 20, and the attribute B has integer values ranging from 1 to 20. Assume that the attributes A and B are independently distributed. The estimated number of tuples in the output of \sigma _{(A > 10)\vee(B=18)}(r) is ____________Q7.
Which of the following relational query languages have the same expressive power? I. Relational algebra II. Tuple relational calculus restricted to safe expressions III. Domain relational calculus restricted to safe expressionsQ8.
The relational algebra expression equivalent to the following tuple calculus expression: \left\{t \mid t \in r \land \left(t[A] = 10 \land t[B]=20\right)\right\} is