Predicate Logic and Popular Culture (Part 29): Grease


Let W(x) be the proposition “I want x.” Translate the logical statement

W(\hbox{you}) \land \forall x(x \ne \hbox{you} \Longrightarrow \lnot W(x)),

where the domain is all people.

The clunky way of translating this into English is, “I want you, and I don’t want anyone who isn’t you.” But it sounds a lot better when John Travolta and Olivia Newton-John sing it.

For professional mathematicians (as opposed to students first learning predicate logic), the more compact way of writing this would be

W(\hbox{you}) \land \exists! x W(x).

green line

Context: This semester, I taught discrete mathematics for the first time. Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

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