Discussion
For a relation R(A, B, C) with three attributes A, B and C, what is the maximum number of possible composite keys ?
Answer: B
The maximum number of composite keys is 4.
A composite key is a key made of two or more attributes. From three attributes the possible combinations of two or more are:
\[ \begin{aligned} &\{A,B\},\ \{A,C\},\ \{B,C\} \\ &\{A,B,C\} \end{aligned} \]
That is \(\binom{3}{2} + \binom{3}{3} = 3 + 1 = 4\). 3 counts only the two-attribute pairs, 7 counts every non-empty subset including the three single attributes, which are not composite, and 9 matches no count.
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