Formalizing Set Theory

See: Formalizing Predicate Logic, Set Theory

Example

Formalize the following without set builder notation

  1. The set of tall students who like basketball

\text{Students} \cap \text{Cdn} \cap (\text{LikeVolleyball} \cup \text{LikeHockey})

Example

Formalize the following without set builder notation as WFF:

  1. No one from Shrek's Swamp has a favourite colour blue

& \text{FromShreksSwamp} \cap \text{FavColBlue} = \emptyset \
& \text{FavColBlue} \subseteq \text{FromShreksSwamp}^\complement
\end

\begin{align}
& (\text{LikeHockey} \cup \text{LikeBaskemtball}) - \text{FavColRed} \subseteq \text{FromOhio} \
& (\text{LikeHockey} \cup \text{LikeBaskemtball}) \cap \text{FavColRed}^\complement \subseteq \text{FromOhio}
\end

Formalizing Relations

See Relations

Example

Using the following sets:

Formalize these sentences:

  1. All houses that are rented are ownedor
  2. Not every student owns a houseorthis one assumes that
  3. Students who rent houses do not own any dwellings

\op{dom}(\text{Students} \triangleleft \text{rents} \triangleright \text{Houses}) \triangleleft \text{owns} = \emptyset

\text{owns} \triangleright \text{Houses} \subseteq \text