Understanding 3NF: plain English please

Question

I am working through an example problem in which we are trying to identify which of the following relations is in Third Normal Form (3NF). Here are the relations we are given:

Answer 1

Let me explain in simple words:

For the given relation, R1(ABCD),the functional dependencies are:

ACD -> B

AC -> D

D -> C

AC -> B

Condition to be in 3NF

X->Y here X is a Super key when Y is non-prime attribute else it can be any attribute

Prime attributes are the attributes which belongs to the super key

Non-prime attributes are the attributes which do not belongs to the super key

Let us come back to relation R1,

AC+=ABCD

AD+=ABCD

ACD+=ABCD and

D+=DC

Thus,we get AD,AC,ACD as our Super keys

And A,C,D are prime attributes and B is a non-prime attributes

ACD->B

This Functional dependency is in 3NF as ACD is a super key and B is prime attribute

AC->D

This Functional dependency is also in 3NF as AC is a super key and D is prime attribute

D->C

This Functional dependency is also in 3NF as D is a prime attribute and C is also prime attribute

AC->B

This Functional dependency is also in 3NF as AC is a super key and B is non-prime attribute

  Thus,the relation is not in 3NF only when non-prime attributes
  does not depend on super key

Hope,this helps!