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    <p>The subtle difference is that 3NF makes a distinction between key and non-key attributes (also called <em>non-prime</em> attributes) whereas BCNF does not.</p> <p>This is best explained using <a href="http://www.cs.ucla.edu/~zaniolo/papers/tods82b.pdf" rel="noreferrer">Zaniolo's definition</a> of 3NF, which is equivalent to Codd's:</p> <blockquote> <p>A relation, R, is in 3NF iff for every nontrivial FD (X->A) satisfied by R at least ONE of the following conditions is true:</p> <p>(a) X is a superkey for R, <strong>or</strong></p> <p>(b) A is a key attribute for R</p> </blockquote> <p>BCNF requires (a) but doesn't treat (b) as a special case of its own. In other words BCNF requires that every nontrivial determinant is a superkey even its dependent attributes happen to be part of a key.</p> <blockquote> <p>A relation, R, is in BCNF iff for every nontrivial FD (X->A) satisfied by R the following condition is true:</p> <p>(a) X is a superkey for R</p> </blockquote> <p>BCNF is therefore more strict.</p> <p>The difference is so subtle that what many people informally describe as 3NF is actually BCNF. For example, you stated here that 3NF means "data depends on the key[s]... and nothing but the key[s]", but that is really an informal description of BCNF and not 3NF. 3NF could more accurately be described as "<em>non-key data</em> depends on the keys... and nothing but the keys".</p> <p>You also stated:</p> <blockquote> <p>the 3NF quote explicitly says "nothing but the key" meaning that all attributes depend solely on the primary key.</p> </blockquote> <p>That's an oversimplification. 3NF and BCNF and all the Normal Forms are concerned with <em>all</em> candidate keys and/or superkeys, not just one "primary" key.</p>
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    1. PODifference between 3NF and BCNF in simple terms (must be able to explain to an 8-year old)
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    1. COWow. Prof. Zaniolo actually teaches my class (CS 143, UCLA), and I stumbled upon this answer while preparing for the final exam. Great to see my prof's name, and thanks for the detailed answer!
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    2. COcould you give an example of a relation which is in 3NF but not in BCNF? its hard for me to imagine...
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    3. COR{A,B,C} where {A,B} is a key. Given the dependency C->B, R satisfies the requirements of 3NF but not BCNF.
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