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Form the following instance of a relation schema $R(A,B,C)$, we can conclude that:

 A B C $1$ $1$ $1$ $1$ $1$ $0$ $2$ $3$ $2$ $2$ $3$ $2$
1. $A$ functionally determines $B$ and $B$ functionally determines $C$
2. $A$ functionally determines $B$ and $B$ does not functionally determine $C$
3. $B$ does not functionally determine $C$
4. $A$ does not functionally determine $B$ and $B$ does not functionally determine $C$
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"Form the following instance of a relation schema R(A,B,C)"
Relation = one table
Instance = values at one moment ( as opposed to the schema, which is the description of all possible values)

Ans. $C$

Generally Normalization is done on the schema itself.

From the relational instance given,we may strike out $FD$ s that do not hold.

e.g. $B$ does not functionally determine $C$(This is true).

But we cannot say that A functionally determines B for the entire relation itself.This is because that , $A->B$ holds for this instance,but in future there might be some tuples added to the instance that may violate $A->B$.

So overall on the relation we cannot conclude that $A->B$,from the relational instance which is just a subset of an entire relation.
edited by

• If we observe carefully "Instance" of a relation Schema R(A,B,C) is given here.

Now as we can see A functionally determines B for the present tuples.

But B does not determines C. That is clearly Visible.

• In future there may be chances of tuples to be present where A can not determine B uniquely.

So,option C is most suitable.

ans is c

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.

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)
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".

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

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.