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[DMDB] Intuition for FD and NF

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janishutz
2026-07-31 12:20:11 +02:00
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semester4/dmdb/parts/00_relational-model_logic/00_model/01_keys.tex
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\subsubsection{Keys}
\label{sec:relations-keys}
\inlinedefinition[Candidate Key] The minimal set of fields that identify each tuple uniquely
\inlinedefinition[Candidate Key] The minimal set of fields that identify each tuple uniquely (non-duplicate attributes (fields) typically)
\inlinedefinition[Primary Key] A single candidate key, i.e. just a single field.
We mark the primary key using \underline{underlining} in visual \glspl{schema}.
Formally, we write $R(\underline{k : D_k}, a:D_a, b:D_b)$ for a given relation, with all valid instances fulfilling
\[
I \subseteq D_k \times D_a \times D_b \land \forall (k, a, b), (k', a', b') \in I : k = k' \rightarrow (a, b) = (a', b')
I \subseteq D_k \times D_a \times D_b \land \forall (k, a, b), (k', a', b') \in I : k = k' \rightarrow (a, b) = (a', b')
\]
i.e. if the key is equal, so is the rest of the tuple (thus they are one and the same\footnote{\hlhref{https://www.youtube.com/watch?v=tGeSEbYzhBU}{Heidrun is her name}}).