GATE CSE 2017 Set 1 | Question: 41

Question

Consider a database that has the relation schemas EMP(EmpId, EmpName, DeptId), 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.

1. {$t$ | $\exists$u $\in$ EMP(t[EmpName] = u[EmpName] $\wedge$ $\forall$v $\in$ DEPT(t[DeptId] $\neq$ v[DeptId]))}
2. {$t$ | $\exists$u $\in$ EMP(t[EmpName] = u[EmpName] $\wedge$ $\exists$v $\in$ DEPT(t[DeptId] $\neq$ v[DeptId]))}
3. {$t$ | $\exists$u $\in$ EMP(t[EmpName] = u[EmpName] $\wedge$ $\exists$v $\in$ DEPT(t[DeptId] $=$ v[DeptId]))}

Which of the above queries are safe?

• A. I and II only
• B. I and III only
• C. II and III only
• D. I, II and III

Comments

@sachin!

If you have got the solution please post it ..i am alo having same doubt 

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So the fact that DeptId can be null has nothing to do with safety of expressions isn't it? It's just been given to confuse.

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Previous year question from 2001 seems to have a similar format. Options A and D from the previous question were deemed safe, rephrased are similar to options 2 and 3 in the current question. we can only conclude these options to be “safe“ if it is implicitly implied that t is within the range of EMP otherwise they cannot be safe. They both are similarly framed, I guess they both came from some textbook. 

Answer 1

All the above explanations are simply amazing but I want to add one point . One of the simplest way to check whether query is safe or not , one should check whether “free variable” (variable not bounded by quantifiers) is complemented in query or not , if not then it is definitely safe . Hence ans here seems to be D)

Comments

@mohnish  bro can u  elaborate more how?