#### Howdy, Stranger!

It looks like you're new here. If you want to get involved, click one of these buttons!

Options

# Exercise 3 - Chapter 3

edited June 2018

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?

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

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