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Armstrong $(1974)$ proposed systematic approach to derive functional dependencies. Match the following w.r.t functional dependencies:

$\begin{array}{}  & \textbf{List-I}  && \textbf{List -II} \\  \text{a.} &  \text{Decomposition Rule} & \text{i.} & \text{If $X \rightarrow Y$ and $Z \rightarrow W$ then $\{X,Z\} \rightarrow \{Y, W\}$} \\  \text{b.} &  \text{Union rule} & \text{ii.} & \text{If $X \rightarrow Y$ and $\{Y, W\} \rightarrow Z$ then $\{X, W\} \rightarrow Z$} \\  \text{c.} &  \text{Composition rule} & \text{iii.} & \text{If $X \rightarrow Y$ and $X \rightarrow Z$ then $X \rightarrow \{Y, Z\}$} \\  \text{d.} &  \text{Psedudo transitivity rule} & \text{iv.} & \text{ If $X \rightarrow \{Y, Z\}$ then $X \rightarrow Y$ and $X \rightarrow Z$} \\  \end{array}$

Codes:

  1. $\text{a-iii, b-ii, c-iv, d-i}$
  2. $\text{a-i, b-iii, c-iv, d-ii}$
  3. $\text{a-ii, b-i, c-iii, d-iv}$
  4. $\text{a-iv, b-iii, c-i, d-ii}$
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D. a-iv, b-iii, c-i, d-ii

 

Decomposition rule : If x->yz then x->y , x->z

Union rule : If x->y , x->z  then x->yz

Composition rule: if x->y and z->w then xz-> yw

Pseudo transitivity rule : If x-> y and yw->z then xw-> z [ y replace by x].

X→Zhen
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