# How could I use set notation to describe this situation?

Tracts are composed of one or more parcels. There are three types of tracts, A, B, and C. There are three types of parcels, D, E, and F. Parcels of any type may or may not be leased. If at least one parcel in a tract is leased, then the tract is considered leased.

How could this situation be described using set notation? Also, how could I use notation to describe a specific set, e.g., "the set of A and B tracts containing leased D parcels," or, "the set of tracts of any type that do not contain leased parcels."

• Is this homework? Or have you genuinely begun to reinvent entity-relationship modelling all for yourself? – Rob Arthan Mar 1 '17 at 23:55
• I'm just asking for help on a personal project. I don't have much knowledge of set theory or entity-relationship modelling. – Patri Mar 2 '17 at 0:17
• fine - and well done! I suggest you look into entity-relationship modelling and then come back to MSE if you have any mathematical questions about it. – Rob Arthan Mar 2 '17 at 0:23

You have sets $T=\{A,B,C\}, P=\{D,E,F\}$ and relation $L$ which is a subset of their Cartesian product.

$$L\subseteq T\times P$$

"the set of A and B tracts containing leased D parcels,"

$$\{t\in \{A,B\}: (t,D)\in L\}$$

or, "the set of tracts of any type that do not contain leased parcels."

$$\{t\in T:\neg\exists p \in P~[(t,p)\in L]\}$$

For further details, research set builder notation and relational databases (entity-relation models )

• Awesome, thanks Graham! – Patri Mar 2 '17 at 1:17