Problem $2.$ Consider a coffee dataset collected by Grind Co Coffee roaster to decide their recipe. They

collected from an experiment measuring three attributes: roast level $(9$ means darkest, $0$ means lightest$),$

aroma intensity $($higher the more intensive$),$ and bean size $($in mm$).$ Each attribute is described and rounded

by a natural number.

$(1)$ Given an experiment measure that is described by the three attributes above, write the concise Cartesian

product set in the format of element $|$ condition

$(2)$ Given the experiment collected data in the following table, write a vector representation of each instance

in the following dataset.