Questions regarding second normal form
If all your dependencies are those you have shown: {A-&gt;GH, B-&gt;IJ, C-&gt;A, F-&gt;B, FC-&gt;DK, K-&gt;E} then you have come to the wrong conclusion.

Your only candidate key is CF. The C and F are not candidate keys on their own.

Therefore, the F-&gt;B dependency (and the C-&gt;A as well) means that the relation violates 2NF.



For the other question, if you had for example these dependencies:

BC -&gt; AF
AF -&gt; BC
 F -&gt; DE


where the candidate keys are BC and AF, then again the F -&gt; DE would mean that the relation violates 2NF. To be in 2NF would mean that there is no dependency on any part of any candidate key.