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I will state the complete question now, since it did not fit in the title.

Is the statement given below correct?

A necessary condition for a relation to be in 2NF but not in 3NF is that some non-prime attribute must be determined by a non-prime attribute or a set containing a non-prime attribute.


This is how I view the above statement:

Breaking the statement into parts:

  1. A necessary condition for a relation to be in 2NF is that some non-prime attribute must be determined by a non-prime attribute or a set containing a non-prime attribute.
  2. A necessary condition for a relation to not be in 3NF is that some non-prime attribute must be determined by a non-prime attribute or a set containing a non-prime attribute.

I will conclude that the statement is correct if and only if both the parts of the statement are individually correct.

Is my view of the statement correct?

If it is correct, then

Part two of the statement fails 3NF test, therefore making part two true.

Part one of the statement does not necessarily mean that the relation is in 2NF, therefore making part one false, because every non-prime attribute $A$ in $R$ may not be fully functionally dependent on every key of R.

So the statement should be false.


What I understand about necessary and what I understand about sufficient condition is this

A necessary condition is a condition that must be present for an event to occur. A sufficient condition is a condition or set of conditions that will produce the event. A necessary condition must be there, but it alone does not provide sufficient cause for the occurrence of the event. Only the sufficient grounds can do this. In other words, all of the necessary elements must be there.

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