Predicate Logic and Popular Culture (Part 11): Garth Brooks

Let $F(x)$ be the proposition “I am friends with $x$,” and let $L(x)$ be the statement $x$ is in low places.” Translate the logical statement

$\exists x(F(x) \land L(x) \land \exists y(x \ne y \land F(y) \land L(y)))$,

where the domain is all people.

The clunky way of translating this into English is, “There is someone who is a friend of mine who is in low places who isn’t another friend of mine in low places.” Of course, this sounds a lot better when Garth Brooks sings it.

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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