Gate2017 cs Q45

45Consider a database that has the relation schemas EMP (EmpId, EmpName, DepId), and DEPT(DeptName, DeptId). Note that the DepId can be permitted to be NULL in the relation EMP. Consider the following queries on the database expressed in tuple relational calculus.
I. {t | ∃ u ∈ EMP (t[EMPName] = u[EmpName] ∧ ∀ v ∈ DEPT (t[DeptId] ≠ DeptId]))}
II. {t | ∃ u ∈ EMP (t[EMPName] = u[EmpName] ∧ ∃ v ∈ DEPT (t[DeptId] ≠ DeptId]))}
III. {t | ∃ u ∈ EMP (t[EMPName] = u[EmpName] ∧ ∃ v ∈ DEPT (t[DeptId] = DeptId]))}

Option : D
Explanation : Given, DepId can be permitted to be NULL
I. {t | ∃ u ∈ EMP (t[EMPName] = u[EmpName] ∧ ∀ v ∈ DEPT (t[DeptId] ≠ DeptId]))} : Gives empnames who donot belong to any department
II. {t | ∃ u ∈ EMP (t[EMPName] = u[EmpName] ∧ ∃ v ∈ DEPT (t[DeptId] ≠ DeptId]))} : Gives empnames who donot belong to some department
III. {t | ∃ u ∈ EMP (t[EMPName] = u[EmpName] ∧ ∃ v ∈ DEPT (t[DeptId] = DeptId]))}: Gives empnames who donot belong to same department
All of these queries are giving some results which are finite and thus all are safe expressions.
Therefore, option D is correct.

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