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# ISRO | ISRO CS 2017 | Question 15

Consider the following table : Faculty (facName, dept, office, rank, dateHired)

facNamedeptofficerankdateHired
RaviArtA101Professor1975
MuraliMathM201Assistant2000
NarayananArtA101Associate1992
LakshmiMathM201Professor1982
MohanCSCC101Professor1980
LakshmiMathM201Professor1982
SreeniMathM203Associate1990
TanujaCSCC101Instructor2001
GaneshCSCC105Associate1995

(Assume that no faculty member within a single department has same name. Each faculty member has only one office identified in office). 3NF refers to third normal form and BCNF refers to Boyee-Codd Normal Form

Then Faculty is

(A) Not in 3NF, in BCNF
(B) In 3NF, not in BCNF
(C) In 3NF, in BCNF
(D) Not in 3NF, not in BCNF

Explanation: There are two non-trivial functional dependencies (FD) in given table:

```facName → dept, office, rank, datehired
office → dept```

Given, Each faculty member has only one office identified in office, that means facName is the primary key (so superkey).

Therefore, FD facName → dept, office, rank, datehired is in 3 NF as well as in BCNF, because facName is the primary key. But FD office → dept is not in BCNF because office is not superkey but dept is in 3 NF as dept is the prime attribute because {dept, rank} is super key.

So, overall relation Faculty is in 3 NF but not in BCNF.

Option (B) is correct.

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