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Exercise 3 - Chapter 3

edited June 2018 in Exercises

Count the number of non-ID columns in Eq. (3.1). Count the number of arrows in Eq. (3.2). They should be the same number; is this a coincidence?

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Equation 3.1

$$ \begin{array}{c|ccc} Employee & FName & WorksIn & Mngr \\ \hline 1 & Alan & 101 & 2 \\ 2 & Ruth & 101 & 2 \\ 3 & Kris & 102 & 3 \end{array} $$ $$ \begin{array}{c|cc} Department & FName & WorksIn & Mngr \\ \hline 101 & Sales & 1 \\ 102 & IT & 3 \end{array} $$ Equation 3.2

Figure

Comments

  • 1.

    I guuss Equation 3.1 should read:

    Equation 3.1

    $$ \begin{array}{c|ccc} Employee & FName & WorksIn & Mngr \\ \hline 1 & Alan & 101 & 2 \\ 2 & Ruth & 101 & 2 \\ 3 & Kris & 102 & 3 \end{array} $$ $$ \begin{array}{c|cc} Department & DName & Secr& \\ \hline 101 & Sales & 1 \\ 102 & IT & 3 \end{array} $$ In which case, the number of non-ID columns is 5, the same as the number of arrows in Equation 3.2. This is not a coincidence, since Equation 3.1 is an instantiation of Equation 3.2. In particular, each non-ID column represents the image of the ID column under a function, which is the instantiation of one of the arrows in Equation 3.2.

    Comment Source:I guuss Equation 3.1 should read: **Equation 3.1** \[ \begin{array}{c|ccc} Employee & FName & WorksIn & Mngr \\\\ \hline 1 & Alan & 101 & 2 \\\\ 2 & Ruth & 101 & 2 \\\\ 3 & Kris & 102 & 3 \end{array} \] \[ \begin{array}{c|cc} Department & DName & Secr& \\\\ \hline 101 & Sales & 1 \\\\ 102 & IT & 3 \end{array} \] In which case, the number of non-ID columns is 5, the same as the number of arrows in Equation 3.2. This is not a coincidence, since Equation 3.1 is an instantiation of Equation 3.2. In particular, each non-ID column represents the image of the ID column under a function, which is the instantiation of one of the arrows in Equation 3.2.
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