54 votes 54 votes From the following instance of a relation schema $R(A,B,C)$, we can conclude that: $$\begin{array}{|l|l|}\hline \textbf{A} & \textbf{B} & \textbf{C} \\\hline \text{1} & \text{1} & \text{1} \\ \text{1} & \text{1} & \text{0} \\ \text{2} & \text{3} & \text{2} \\ \text{2} & \text{3} & \text{2} \\\hline \end{array}$$ $A$ functionally determines $B$ and $B$ functionally determines $C$ $A$ functionally determines $B$ and $B$ does not functionally determine $C$ $B$ does not functionally determine $C$ $A$ does not functionally determine $B$ and $B$ does not functionally determine $C$ Databases gatecse-2002 databases database-normalization + – Kathleen asked Sep 15, 2014 edited Apr 17, 2019 by Pooja Khatri Kathleen 16.6k views answer comment Share Follow See all 11 Comments See all 11 11 Comments reply Show 8 previous comments rajankakaniya commented Nov 14, 2021 i edited by rajankakaniya Nov 14, 2021 reply Follow Share https://gateoverflow.in/855/Gate-cse-2002-question-2-25?show=158863#c158863 check Arjun sir’s comment above. FD is defined on schema (not on instance). So, we have to think that way. From a particular instance we can only comment about FD that do not hold. We can not comment about FD that holds because in future instance may change. Also thanks to Deepak Sir for teaching this. 3 votes 3 votes Nithesh_Cray commented Apr 20, 2022 reply Follow Share Whenever instance of a relation is given we canot say a → b,but we can say a !→ b. 0 votes 0 votes ChayAdhiraj commented Jan 29, 2023 reply Follow Share GATE 2000 also had a similar question with instance mentioned. But there they wanted a definite answer ! https://gateoverflow.in/671/gate-cse-2000-question-2-24 1 votes 1 votes Please log in or register to add a comment.
–2 votes –2 votes When value of A is 1,B is 1.When value of A is 2,B is 3.So A functionally determines B. When value of B is 1,C is 1 and in another case C is 0.So B does not functionally determine C. Hence,the answer is B. Manjeel Goswami answered Nov 2, 2016 Manjeel Goswami comment Share Follow See all 2 Comments See all 2 2 Comments reply suvasish pal commented Jul 16, 2017 reply Follow Share wrong answer. 0 votes 0 votes Jason GATE commented Jan 2, 2018 reply Follow Share KINDLY HIDE THIS ANSWER 0 votes 0 votes Please log in or register to add a comment.
–3 votes –3 votes Ans will be B Here A->B satisfies(for same value in A , B also gives unique value) B->C not satisfies(when B is 1 , C gives two values 1,0) srestha answered Sep 11, 2015 srestha comment Share Follow See all 4 Comments See all 4 4 Comments reply Arjun commented Nov 21, 2015 reply Follow Share For the given instance yes, but there can be another instance also for R where the FD may not hold. So, from a given instance we can only say "no FD". 7 votes 7 votes set2018 commented Oct 9, 2017 reply Follow Share srestha @Arjun sir question says ,Form the following instance of a relation so according to that B should be answer .why we are considering other possibilities ?pls clear this 0 votes 0 votes Arjun commented Oct 9, 2017 reply Follow Share Suppose a person from religion X throws a bomb. From this can we conclude that religion X is teaching terrorism? Likewise everything depends on the definition. FD is defined on relational schema and not on any instance alone. 11 votes 11 votes Lakshman Bhaiya commented Nov 21, 2018 reply Follow Share If they say $"$given relation(schema)$"$ then answer should be $(B)?$ please correct me if I'm wrong$?$ 1 votes 1 votes Please log in or register to add a comment.