Project ForgeGiven the following two statements:
S1: Every table with two single-valued attributes is in 1NF, 2NF, 3NF and BCNF. S2: AB→C, D→E, E→C is a minimal cover for the set of functional dependencies AB→C, D→E, AB→E, E→C.
Which one of the following is CORRECT?
- S1 is TRUE and S2 is FALSE.
- BBoth S1 and S2 are TRUE.
- CS1 is FALSE and S2 is TRUE.
- DBoth S1 and S2 are FALSE.
Explanation
S1 is TRUE: with only two attributes, any non-trivial FD between them must have one determining the other, making that attribute a superkey (satisfying BCNF, hence every weaker normal form too) — there's no way to fit a partial or transitive dependency into just two attributes. S2 is FALSE: the proposed cover {AB→C, D→E, E→C} does NOT have the same closure as the original set — computing (AB)⁺ under the proposed cover gives only {A,B,C} (AB→C, and C determines nothing further), which does not include E, so AB→E is NOT derivable from the proposed cover even though it was one of the original dependencies. The two sets aren't equivalent, so it isn't a valid cover at all (let alone a minimal one).
Source: GATE CS 2014 (Session 1) (2014)
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