95 votes 95 votes 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? $\left\{e.name \mid employee(e) \wedge \left(\forall x\right)\left[\neg employee\left(x \right) \vee x.supervisorName \neq e.name \vee x.sex = ``male" \right]\right\}$ Names of employees with a male supervisor. Names of employees with no immediate male subordinates. Names of employees with no immediate female subordinates. Names of employees with a female supervisor. Databases gatecse-2007 databases relational-calculus normal + – Kathleen asked Sep 21, 2014 Kathleen 23.3k views answer comment Share Follow See all 5 Comments See all 5 5 Comments reply Show 2 previous comments KUSHAGRA गुप्ता commented Oct 28, 2019 i edited by KUSHAGRA गुप्ता Jan 8, 2020 reply Follow Share $\{e.name|employee(e)\wedge \forall (x)[(employee(x)\wedge x.supervisorName=e.name)\rightarrow x.sex=male]\}$ Print the names of those employees who are a supervisor but should not be a supervisor of a female employee Ans: C: Names of employees with no immediate female subordinates. 11 votes 11 votes Deepak Poonia commented Nov 13, 2023 reply Follow Share Detailed Video Solution: https://youtu.be/RgNpwKnGWPU 2 votes 2 votes Shukla_ commented Nov 27, 2023 i edited by Shukla_ Nov 27, 2023 reply Follow Share we can rewrite P → Q as ¬P V QSo we can rewrite it as ∀x(employee(x) → (x.supervisorname≠e.name V x.sex=”male” )Or ∀x ∈ employee(x) (x.supervisorname≠e.name V x.sex=”male”)Or ∀x ∈ employee(x)( ¬(x.supervisorname=e.name) V x.sex=”male”)Or ∀x ∈ employee(x)( x.supervisorname=e.name → x.sex=”male”)So TRC query will be {e.name | employee(e)∧ ∀x∈employee(x)( x.supervisorname=e.name → x.sex=”male”) which gives those employee names for which if they are supervisor then they are the supervising only male employees. Hence Option C 0 votes 0 votes Please log in or register to add a comment.
Best answer 225 votes 225 votes OR ($\vee$) is commutative and associative, therefore i can rewrite given query as: $\left\{e.name \mid employee(e) \wedge \left(\forall x\right)\left[\neg employee\left(x \right) \vee x.sex = ``male" \vee x.supervisorName \neq e.name \right]\right\}$ $\left\{e.name \mid employee(e) \wedge \left(\forall x\right)\left[\neg (employee\left(x \right) \wedge x.sex \neq ``male") \vee x.supervisorName \neq e.name \right]\right\}$ $\left\{e.name \mid employee(e) \wedge \left(\forall x\right)\left[ (employee\left(x \right) \wedge x.sex \neq ``male") \Rightarrow x.supervisorName \neq e.name \right]\right\}$ $\left\{e.name \mid employee(e) \wedge \left(\forall x\right)\left[ (employee\left(x \right) \wedge x.sex =``female") \Rightarrow x.supervisorName \neq e.name \right]\right\}$ It is clear now they are saying something about female employees, This query does not say anything about male employees. Therefore Option A and B are out of consideration. This query retrieves those $e.name$ who satisfies this condition: $\forall x [(employee(x)\wedge x.sex="female")\Rightarrow x.supervisorName\neq e.name]$ Means retrieves those e.name, who is not a supervisor of any female employees. i.e it retrieves name of employees with no female subordinate. (here "immediate" is obvious, as we are checking first level supervisor.) Hence, option C. Sachin Mittal 1 answered Dec 12, 2016 edited Jun 22, 2018 by Milicevic3306 Sachin Mittal 1 comment Share Follow See all 11 Comments See all 11 11 Comments reply Show 8 previous comments tusharp commented Apr 25, 2019 reply Follow Share Apply De Morgan law after AND condition. For all P(x) == There does not exist ~P(x). It will be simple after that. 0 votes 0 votes Neel123 commented Aug 5, 2022 reply Follow Share Why we are putting () around first two terms only and not the third one in the second step? 0 votes 0 votes sk91 commented Dec 27, 2022 reply Follow Share @Neel123 As mentioned in the answer, $\lor$ is commutative and associative. So, expression $A \lor B \lor C$ can be considered as either $((A \lor B)\lor C)$ (or) $(A\lor(B \lor C))$ 0 votes 0 votes Please log in or register to add a comment.
51 votes 51 votes {e.name∣employee(e)∧(∀x)[¬employee(x)∨x.supervisorName≠e.name∨x.sex=‘‘male"]} ...(1) By Using De-morgan's law We can write expression ∀x(P(X)) as NOT ∃x(NOT P(X)). Using this concept, we rewrite the conditon (1) as given in question above {e.name∣employee(e)∧ NOT(∃x)[employee(x) ^ NOT x.supervisorName≠e.name ^ NOT x.sex=‘‘male"]} ...(2) Considering only 2 genders are represented in the database as either male or female we can again rewrite expression (2) as {e.name∣employee(e)∧ NOT(∃x)[employee(x) ^ x.supervisorName = e.name ^ x.sex=‘‘female"]} ...(3) Now it is easier to read the expression above. It Says, for a tuple of employee, there must not be a case that this employee being considered is supervisor of some female employee. That means it selects all those employee who do not supervise any female employee hence do no have any immediate female sub-ordinate. Hence, Ans (C) Ayush Upadhyaya answered Oct 3, 2017 Ayush Upadhyaya comment Share Follow See all 10 Comments See all 10 10 Comments reply iarnav commented Nov 30, 2017 reply Follow Share @Ayush Upadhyaya Can you please explain these one by one in simple English - employee(x) x.supervisorName = e.name x.sex=‘‘female" 0 votes 0 votes Ayush Upadhyaya commented Nov 30, 2017 reply Follow Share I am not able to get your statement s Iarnav. Could you tell me where are you facing problem in understanding the solution above? It's just a simple application of de-morgan's law for quantifiers that I have Used. Still if you have any trouble, let me know. Happy to help. :) 0 votes 0 votes iarnav commented Dec 1, 2017 reply Follow Share @ Ayush Upadhyaya In eq 3, what does the below line means? Can you tell it in Hindi? I mean, does it mean - Koi bhi Supervisor aur employee ka naam same nai hai and jo supervisor hai woh female nai hai kyunki bracket ke bahar NOT likha hai? x.supervisorName = e.name ^ x.sex=‘‘female" 0 votes 0 votes Ayush Upadhyaya commented Dec 1, 2017 reply Follow Share @Iarnav- {e.name∣employee(e)∧ NOT(∃x)[employee(x) ^ x.supervisorName = e.name ^ x.sex=‘‘female"]} (∃x)[employee(x) ^ x.supervisorName = e.name ^ x.sex=‘‘female"] The highlighted text means tumne ek randomly employee table se tuple select kra aur check kra ki uska supervisor ka naam is same as the tuple 'e'( ie. e.name) jo consider kra h and yeh jo tuple x hai wo female employee ka hona chahiye. Means, you select an employee jo kisi female employee ka boss hai. matlab female employee isko report krti h Now notice that there is a not symbol also in eq 3. This implies that wo saare employee de do jo kisi bhi female employee k boss na ho means koi b female employee inhe report nahi karti. This is good trick in logic to write expression for "none" kind of statements. Example : Consider x to be domain of all people in world and B(X) be the predicate that x is best in this world. Now you write "Someone is best in this world" as ∃x(B(X)). Now, this ∃x becomes false when there is not even a single value of x which satisfies a predicate. matlab x ko manlo can take domain values as x1,x2,x3 then ∃x(B(X)) = (B(x1) v B(x2) v B(x3) ) koi b x1,x2,x3 k liye agar B(X) true hua toh ∃x(B(X)) true hoga. agar kisi k liye nahi hua toh ∃x(B(X)) is false. So when you place not in it, ∼ ∃x(B(X)) = ∀x(∼B(x1) ^ ∼B(x2) ^ ∼B(x3) ) and this becomes "No one is best in this world" I hope kch smajh aya hoga 14 votes 14 votes iarnav commented Dec 1, 2017 reply Follow Share @ Ayush Upadhyaya Yes, thank you, brother. 0 votes 0 votes lakshaysaini2013 commented Oct 25, 2018 reply Follow Share @Ayush Upadhyaya thank you sir it helps me to understand this question 0 votes 0 votes SomeEarth commented Jan 13, 2019 reply Follow Share @Ayush Upadhyaya sir, can we use Venn diagram Approach in order to understand query so that we need not to transform the query into simpler form (Although that method is far superior ) OR will that will be too complex (considering the time constraint of exm) . 0 votes 0 votes Ayush Upadhyaya commented Jan 14, 2019 reply Follow Share @SomeEarth-if you have that method, please share fast, we are always in search of better methods. :) I am not sure about whether venn diagram method will work here. 0 votes 0 votes SomeEarth commented Jan 14, 2019 reply Follow Share while i was writing the earlier comment I tried my level best to visualize the inner query and try to present u but I wasn't able to do that so I thought to share that idea with u. (but unfortunately we all are running short on time so I guess I'll do the Brainstroming on this after Gate on this q and for other question as well. (Multiple possible answer for any question makes it easier to Understand ) ((as u and other Senior member of GO community are doing)) 0 votes 0 votes KunuSwavik commented Oct 23, 2021 reply Follow Share @ayush sir , I didn't get the term " x.supervisorName = e.name" can you please elaborate ? 0 votes 0 votes Please log in or register to add a comment.
38 votes 38 votes Query is selecting e such that e is an employee and for all x, either x is not an employee or x's supervisor's name is not e.name or x is male. So, this is equivalent to saying, select all employees who don't have an immediate female subordinate. (Assuming there is no transgender). (C) option. Arjun answered Dec 18, 2014 Arjun comment Share Follow See all 16 Comments See all 16 16 Comments reply Show 13 previous comments smelly indian commented Sep 10, 2017 i reshown by smelly indian Sep 10, 2017 reply Follow Share x's supervisor's name is not e.name, can someone explain me this line. 0 votes 0 votes Anu007 commented Jan 5, 2018 reply Follow Share wait for a day i will explain with example. 0 votes 0 votes VYAN_jy commented Oct 16, 2022 reply Follow Share I think it means either e is not a supervisor of any employee and if he/she is then his subordinate is male only. 0 votes 0 votes Please log in or register to add a comment.
6 votes 6 votes Apply de morgen laws and then simplify as follows. jatin saini answered Jan 11, 2017 jatin saini comment Share Follow See all 0 reply Please log in or register to add a comment.