Predicate Logic and Popular Culture (Part 47): Zac Brown Band

Let F(x) be the proposition “x is a good friend,” let S(x) be the proposition “x lives down the street,” let G(w) be the proposition “w is a good-looking woman,” let A(w) be the proposition “w has her arms around me,” let p be the proposition “I am in a small town where it feels like home,” let N(x) be the proposition “I have x,” and let H(x) be the proposition “I need x.” Translate the logical statement

\exists x_1 \exists x_2(F(x_1) \land F(x_2) \land S(x_1) \land S(x_2) \land x_1 \ne x_2)

\land \exists w(G(w) \land A(w)) \land p \land \forall x (N(x) \Leftrightarrow H(x)).

I think this is a reasonable translation of the chorus of one of country music’s big hits from 2015.

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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  1. Predicate Logic and Popular Culture: Index | Mean Green Math

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