title: BCNF: Looking for example that actually uses superkey instead of candidate key
body: <p>The definition of the Boyce–Codd normal form states that the determinants of all non-trivial functional dependencies have to be superkeys.</p>
  
  <p>All the examples for relations in BCNF I found make use of candidate keys. I am looking for an example that actually has a superkey as determinant which is not a candidate key.</p>
  
  <p>I fail to come up with a relation that only uses superkeys which can't be transformed to use candidate keys.</p>
  
  <p>Let's say we have a relation with an candidate key and an additional functional dependency with a superkey as determinant.</p>
  
  <pre><code>R1(A,B,C)
  {A}
  A,B -&gt; C
  </code></pre>
  
  <p>This additional FD is redundant because it contains an candidate key that obviously detemines the other attribute (A -> C).</p>
  
  <p>Trying to build another example with two candidate keys is also useless.</p>
  
  <pre><code>R2(A,B,C,D)
  {A,B},{B,C}
  A,B,C -&gt; D
  </code></pre>
  
  <p>This has the exact same problem as above.</p>
  
  <p>I am actually wondering if there even is an example without candidate keys. But why would the definition be broader than necessary? Or are the definitions equivalent as the dependencies can always be transformed?</p>