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GATE198812i
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What are the three axioms of functional dependency for the relational databases given by Armstrong.
gate1988
normal
descriptive
databases
databasenormalization
asked
Dec 19, 2016
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Databases
by
jothee

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Best answer
1. AXIOM OF REFLEXIVITY
If $Y\subseteq X$ then $X\rightarrow Y$
2. AXIOM OF AUGMENTATION
If $X\rightarrow Y$ then $XZ\rightarrow YZ$ for any Z
3. AXIOM OF TRANSITIVITY
If $X\rightarrow Y$ and $Y\rightarrow Z$ then $X\rightarrow Z$
answered
Sep 15, 2017
by
Aashish S
selected
Jul 19, 2019
by
Arjun
comment
+1
If $Y\subseteq X$ then $X\rightarrow Y$
$\implies \text{Axiom of reflexivity is also called a trivial functional dependency.}$
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GATE198812iic
Using Armstrong’s axioms of functional dependency derive the following rules: $\{ x \rightarrow y, \: z \subset y \} \mid= x \rightarrow z$ (Note: $x \rightarrow y$ denotes $y$ is functionally dependent on $x$, $z \subseteq y$ denotes $z$ is subset of $y$, and $\mid =$ means derives).
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GATE198812iib
Using Armstrong’s axioms of functional dependency derive the following rules: $\{ x \rightarrow y, \: wy \rightarrow z \} \mid= xw \rightarrow z$ (Note: $x \rightarrow y$ denotes $y$ is functionally dependent on $x$, $z \subseteq y$ denotes $z$ is subset of $y$, and $\mid =$ means derives).
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GATE198812iia
Using Armstrong’s axioms of functional dependency derive the following rules: $\{ x \rightarrow y, \: x \rightarrow z \} \mid= x \rightarrow yz$ (Note: $x \rightarrow y$ denotes $y$ is functionally dependent on $x$, $z \subseteq y$ denotes $z$ is subset of $y$, and $\mid =$ means derives).
asked
Dec 19, 2016
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Databases
by
jothee

225
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gate1988
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databasenormalization
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GATE198812iv
Select SNAME from S Where SNOin (select SNO from SP where PNOin (select PNO from P Where COLOUR='BLUE')) What relations are being used in the above SQL query? Given at least two attributes of each of these relations.
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Dec 20, 2016
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gate1988
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